related rates and implicit differentiation calculator. One common method for solving such a problem is to begin with implicit differentiation …. Directional Derivative Calculator with Steps & Solution. Many words in English are made up of a single free morpheme. Calculate the rate at which the distance between the cat and dog was changing three seconds into their run. 3 Implicit Tangents and Derivatives 7. A "related rates'' problem is a problem in which we know one of the rates of change at a given instant—say, x ˙ = d x / d t —and we want to find the. dy implicit differentiation to solve for. Write down any numerical facts known about the variables. It explains how to use implicit differentiation to find dy/dt and dx/dt. Apply implicit differentiation and solve for related rates. , ae (Implicit differentiation Derivative of the inverse of a function (including Higher order derivatives Corresponding characteristics of graphs of f Average and instantaneous rates of change Related rates …. With this process, you can also check where the lower and upper values occur. The first thing that we need to do here is use implicit differentiation to differentiate the equation with respect to t t. Velocity is the rate of change of a function. Calculate the Difference Between Two Columns in a Pivo…. The general pattern is: Start with the inverse equation in explicit form. Suppose you are differentiating with respect to x x x. and implicit differentiation…. Apply implicit differentiation …. Schuyler's clock is kaput; the minute hand functions as it should but the hour hand is stuck at 4. (4) Find the derivatives of the following. 6 Calculating Higher Order Derivatives Unit 3 Derivatives …. Once we have an equation establishing the relationship among the variables, we differentiate implicitly. Any quantity that changes should not be substituted until the derivative is being evaluated at the specific time stated in the question. Aim Colonization is a central topic in ecology and one of the cornerstones of island biogeography. They are in the following order. The following is the typical cost function associated with producing goods. Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40. Riemann Sums and Definite Integrals; Implicit Differentiation. 1 Differentiation with Parameters 7. To calculate the derivative y′ y ′ of an implicit function: Treat the variable y y in the relation as an unknown but differentiable function of x x (like y =g(x) y = g ( x) ), and differentiate …. 1 x2y+xy2=6 2 y2= x−1 x+1 3 x=tany 4 x+siny=xy 5 x2−xy=5 6 y=x 9 4 7 y=3x 8 …. Plug in all the values you know, leaving only the one you’re solving for. One of them starts walking north at a rate so that the angle shown in the diagram below is changing at a constant rate of 0. Use implicit di erentiation to determine the slope of the graph of y2 = 3xy 5 where y = 1. This problem has been solved! See the answer. An interactive exploration of related rates, the study of variables that change over time where one variable is expressed as a function of the other. Derivative by Definition Square Roots. This is vague, so it’s best to look directly at how to solve a related rate …. Unit #5 : Implicit Diﬀerentiation, Related Rates Goals. For instance, if you differentiate …. AP Calculus SCHOLARS, Tuesday, MAY 4, 2021!! LESSON VIDEOS & OLD TESTS. Students will find the second derivative …. x y= 2 Question 6 A curve is described by the implicit …. When the cloud has moved to the right. The key idea behind implicit differentiation is to assume that y is a function of x even if we cannot explicitly solve for y. IMPLICIT DIFFERENTIATION 121 Example 2. , with independent variable of the form x (or some other symbol), and dependent variable of the form y (or some other symbol). Session 13: Implicit Differentiation. Solved: Use implicit differentiation …. ©v X2G0Z1E4i fKpuBt5ay ES HoXfxt mwXaPr HeX DLnL vC 2. The procedure to use the average rate of change calculator …. Free Response - 50% of your score. 8 Implicit Differentiation (Lecture 10) – CALCULUS I MA…. -Informal question/ answer sessions -Group Work -Quiz / Short Test -Graphics Calculator …. Limit calculations, including limits involving infinity, Continuity Derivative of a composite function (chain rule), e. water drains from a cone (related rates problem). With these codelets, the executor implements the Cooley-Turkey FFT Origin can calculate the magnitude, phase and amplitude of the transformed data. We have differentiation tables, rate of change, product rule, quotient rule, chain rule, and derivatives of inverse functions worksheets. The surface area of the top side of the pizza dough is given by. Applications of Differentiation. 6) Lecture 17: Implicit Differentiation (§2. 5 6 2 1/2 12 6 2 1/2 -1/2 5y LINEAR IN y/ — 6T + 5y for y into your solution for part are consistent by substituting the expression Check that your solutions to parts and to get y/ in terms of x. Implicit Differentiation Homework Answers Example 6 - Find the Equation of the Tangent Line Calculus 1: Related Rates (Level: Easy - Hard) Related Rates (KristaKingMath) Calculus - Understanding Implicit Differentiation RELATED RATES: Ladder sliding Page 9/65. All forward-looking statements, express or implied, included in this report and the documents we incorporate by reference and that are …. 1 Related Rates (Method , Examples) 31. Findtheslopeofthegraphatthepoints(1; p 3) and (1; p 3). In these types of problems, one thing changes but we are interested in seeing how something else changes. 11 Linearization and Differentials rule, derivative of inverse functions, rates of change, implicit differentiation, related rates, linearization (optional). The rules of differentiation produce an equation relating the rates of those quantities. EQUATION slope an equation to the tangent line to dy dc = 25 at the point (3, 4). Most implicit relations, such as is defined by the equation 9x2 +y2 =, are not of the required form F(x,y) = 0. Chapter 6: The Instantaneous Rate of Change: Derivative as a Function; Determining derivatives using Commands, the Expression Palettes and the Context Panel; Student[Calculus1] library; Implicit differentiation. Related Rates; Linearization; L'Hospital's Rule; Integrals. The early applications of differentiation …. In all cases, you can solve the related rates problem by taking the derivative of both sides, plugging in all the known values (namely, x, y, and ˙x), and then . This means you need to use the Chain Rule on terms that include y y y by multiplying by d y d x \frac{dy}{dx. Related Rates, Newton's Method, Linear Approximation. Graphing Calculator; DESMOS Activity 1; DESMOS Activity 2; DESMOS Activity 3; Recorded Lectures; Calendar; Videos. A curve has implicit equation x y y y x xy3 3 2+ + + − = +3 3 6 50 2. 11) TI-89 and Implicit Differentiation; Chapter 3. Riemann Sums and Definite Integrals: MATH 151 Problems 6-12 Related rates problems, differentials, linear and quadratic approximations. Derivative Calculator - Take the derivative of a polynomial, trig function, or even more complicated expressions. (1) Find the derivative of y = x cos x Solution. the building at the rate of 2 ft/min. Differentiate each side of the equation by treating y y y as an implicit function of x x x. Using implicit differentiation to find the derivative with respect to time, we get. Geometrically speaking, the derivative of any function at a particular point gives the slope of the tangent at that point of the function. Beyond calculus context, derivative calculator shows the gradient to calculate the derivative problems to rise, the given by the value. This course features a wide range of readings, simulations, assessments. In this problem, we consider the Lemniscate curve (1) (a2+y2)2 =3 (z2 - ) 2 -2 Figure 1: Bernoulli's Lemniscate The goal of this problem is to find the four points of the Lemniscate curve with horizontal tangent lines. Start learning today! Strategy for Solving Related Rates Problems #1. Repeating this process, function y's third order derivative …. •There must be an equation relating the 2(+) quantities. Calculus I - Implicit Differentiation Section 3-10 : Implicit Differentiation Back to Problem List 8. The Derivative from First Principles. Concavity and inflection points 5. Jean-Baptiste Campesato MAT137Y1 - LEC0501 - Calculus! - Oct 24. Time-saving lesson video on Implicit Differentiation with clear explanations and tons of step-by-step examples. Implicit differentiation; Derivative of the inverse of a function (including and ) Related rates of change; Integral Calculus …. What is Related Rates Calculator Symbolab. The trough is a triangular prism 10 feet long, 4 feet high, and 2 feet wide at the top. Course Info: 1st Day Handout: Parent/Student Letter. The graph of $$8x^3e^{y^2} = 3$$ is shown below. Implicit Differentiation - Related Rates Challenge Quizzes Implicit Differentiation: Level 2 Challenges Implicit Differentiation: Level 3 Challenges Implicit Differentiation …. Derivative is used to calculate rate …. Related Rates – The Anxious Panda. Cal_AB_LAP_5_IMPLICIT DIFFERENTIATION AND RELA…. 5) Lesson 13: Derivatives as Rates of Changes (Briggs 3. 4 NO Calculator - 40 min test 1 Thu10/7/2021 2 nd ½ of BLOCK Students will find the derivative of an implicitly defined function. Worked example: Differentiating related functions. Calculus Related Rates Example Volume of Cone. Calculator Reference 4 - Derivatives …. Introducing Maple 19 Single Variable Differential Calculus. At what rate is distance between the two people changing when radians? so $\sec{\theta} = \frac{x}{50}$ and so I hear the next step is:. Limits: MATH 171 Problems 8 & 9 Tangent lines to parametric equations and related rates examples. In calculus, when you have an equation for y written in terms of x (like y = x2 -3x), it's easy to use basic differentiation techniques (known by mathematicians as "explicit differentiation" techniques) to find the derivative…. • derivatives of other trigonometric functions §2. Fundamental Theorem of Calculus and Integration Methods. 3 - Derivatives of Trig Functions: 3. Calculator Online Related Rates. We will continue from there tomorrow. They are also assessed on their ability to solve related rates pro. AP Calculus AB Course Details; Use implicit differentiation to find the derivative …. By observing changing rates students would be able to measure concrete examples and discover their relationships. See the page on implicit differentiation to learn how. In general then, n(t)=2t no – Thus the rate of growth of the population at time t is (dn/dt)=no2tln2 18. 5 Selecting Procedures for Calculating Derivatives 3. The student will implicit differentiation and make substitutions to solve these types of questions. Problem 6b - Calculate the rate …. Search: Implicit Differentiation With Trig. 9 Derivatives of Logarithmic and Exponential Functions. Where To Download Implicit Differentiation Homework Answers down the wall Implicit differentiation COMPLETELY Dy Calculate Dx # Dx For The Relation 3x + Xy = Y. In this tutorial students will learn how to model a related rates problem using parametric equations and a graphing utility. 5 Higher Order Derivative Using Implicit Differentiation; 3. Phone: (773) 809–5659 | Contact. If you labeled a ladder length c, and you know the rate …. The Derivative Calculator supports computing first, second, …, fifth derivatives as well as. 3C: Solve problems involving related rates, optimization, rectilinear motion, (BC) and planar motion. (KristaKingMath) Related Rates in Calculus Implicit Differentiation Examples Implicit Differentiation Showing explicit and implicit differentiation give same result | AP Calculus AB | Khan Academy More implicit differentiationCalculus Lesson 14: 2. Assign variables to anything you have or need to find, and label the picture as so. It means that the function is expressed in terms of both x and y. 1Defining Average and Instantaneous Rates of Change at a Point 2. For this calculus instructional activity, the students solve word problems following 8 different key steps. 00:26:32 – Calculate …. The steps of logarithmic differentiation are outlined below. x 3 d 2 y d x 2 + 6 x 2 d y d x + ( n 2 x 2 + 6) x y = 0. Just behind related rates problems, the topic of implicit differentiation is one of the most difficult for students in a calculus. pdf from MATHEMATIC MATH1201 at University of Technology, Jamaica. Chapter 7 Related Rates and Implicit Derivatives. If you want to evaluate the derivative at the specific points, then substitute the value of the points x and y. 74-75 3 Implicit Differentiation Review 4 QUIZ 1 5 Related Rates (p. Recall: The derivative of x with respect to x is_____ The derivative …. Correct answer: \displaystyle \frac {1} {8 \pi} inches/sec. Implicit differentiation is needed in some applications. Differentiation Techniques in Review - 7. Calculus AB: Sample Syllabus 4. The 2 comes from the derivative of the inner function and then I multiply that by the implicit derivative of x which was given as 3 so I get 6. This is a 5-hour introductory calculus course designed primarily for engineering majors and certain other technical majors. I have this related rates problem, but I keep getting a negative number for dx/dt heres the problem. This assumption does not require any work, but we need to be very careful to treat y as a function when we Calculate …. Session 31: Related Rates. 3 Finding the Derivative of a Function Given its Table of Values; 3. To generalize the above, comparative statics uses implicit differentiation to study the effect of variable changes in economic models. The topics preceded with an asterisk (*) are BC only topics. 4 Intro to related rates In related rates, we are often using implicit differentiation with respect to dt. Implicit differentiation and related rates quiz. The rate of change of the truck is dx/dt = 50 mph because it is traveling away from the intersection, while the rate …. The rate of change of the truck is dx/dt = 50 mph because it is traveling away from the intersection, while the rate of change of the car is dy/dt = −60 mph because it is traveling toward the intersection. 1st Day Homework: Academic Integrity, Parent Survey, Student Survey. I am new to implicit differentiation. S1:E 11 Implicit Differentiation and Related Rates TV-PG | Mar 5, 2010 | 31m The final strategy; implicit differentiation is used when it is difficult to solve a function for y; applying this rule to problems in related rates; the rate …. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Now we need an equation relating our variables, which is the area equation: A = πr2. y = + sqrt ( 7 - x2) and, y = - sqrt (7 - x2). Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. 264 » 24 MB) Implicit differentiation…. u Q BMwatd Ge4 Pw gi It Hhz BIXnrf eisnoi …. Use implicit di erentiation to nd an equation of the tangent line to the curve y2(y2 4) = x2(x2 5) at the point (x;y) = (0; 2). Let f(x)=g(x)/h(x), where both g and h are differentiable and h(x)≠0. Diﬀerentiate both sides of the equation with respect to “x” 2. 11) TI-89 and Implicit Differentiation; Chapter 2. Solved exercises of Implicit Differentiation. Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15. calculate a differential equation, substitute initial conditions, and solve for a missing value. identifying implicit differentiation as a tool to differentiate functions where one variable is difficult to isolate; explaining the relationship between implicit differentiation and the chain rule; calculating related rates for the time derivatives …. com/patrickjmt !! Buy my book!: '1001 Calcul. The fact that dy/dt is negative means that the distance from the top of the ladder to the ground decreases at a rate of 0. Now, select a variable from the drop-down list in order to differentiate with respect to that particular variable. Implicit Differentiation (7:55) The Rate of Change (6:53) Related Rates (8:31) All videos are closed captioned. Beyond Calculus is a free online video book for AP Calculus AB. Related rates problems can be solved using by computing. Extrema on an Interval; Rolle’s Theorem; Mean Value Theorem 8. So for hyperbolic trig functions we have the hyperbolic cosine and the hyperbolic sine. When more than one derivative is applied to a function, it is consider higher order derivatives. How long is the ladder? This is a fairly common example of a related rates problem and a common application of derivatives and implicit differentiation. The chain rule is the key to solving such problems. The steps involved in solving a related rates problem can be summarized as: 1. Rate of the spread of a rumor in sociology. Related Rates Example 1 Air is being pumped into a spherical balloon at a rate of 5 cm 3/min. 2 - Activity 2 - Graphs of Functions and their Derivatives. Then the word rate means a derivative with respect to time. If possible, we subsequently solve for dy dx d y d x using algebra. Derivative of a Constant Multiple of a Function. 1C Calculate derivatives implicit differentiation related rate implicit differentiation related rates parametric algebraic logarithmic LO 2. RELATED RATES – Cone Problem (Water Filling and Leaking) Water is leaking out of an inverted conical tank at a rate of 10,000 at the same time water is being pumped into the tank at a constant rate. Furthermore, you’ll often find. The Derivative: Derivatives of Polynomials and Exponentials Product and Quotient Rules Derivatives of Trig Functions The Chain Rule Implicit Differentiation Logarithmic Differentiation Derivatives in the Sciences Exponential Growth and Decay Related Rates …. Plug in all the values you know, leaving only the one you're solving for. 7 Derivatives of Inverse Functions (Lecture 9) CALCULUS I MAT 301 - 0509. Inflation has its pros and cons, yet it is a normal part of a healthy economy. “In mathematics, a derivative is the rate of change of a function with respect to a variable. The vertical displacement remains constant at 50m. 07 Derivatives with Calculator…. $$displaystyle int (2x+1)^2dx$$ $$displaystyle int xsqrt{2x+3}dx$$ \(displaystyle int. 4 Implicit Differentiation (Section 3. True False Working with related rates of change is similar to implicit di erentiation in that we are nding the derivative …. Implicit Differentiation Calculator - Free Onli…. We will now use implicit differentiation on both sides with respect to t. This course is in content deeper and broader than AP Calculus AB course, suitable for the students who are intended in majoring in math, science, …. Using implicit differentiation …. In most related rates problems, we have an equation that relates derivative of both sides with respect to t (implicit differentiation). 5, we have the following equations. AP Calculus AB Related Rates and Implicit Differentiation Review Problem Set 1. The implicit differentiation calculator will find the first and second derivatives of an implicit function treating either y as a function of x or x as a function of y, with steps shown. The derivative of a function f at a number a is denoted by f' ( a ) and is given by: So f' (a) represents the slope of the tangent line to the curve at a, or equivalently, the instantaneous rate …. Calc Final Thursday!!! taking calc in college. [To see the graph of the corresponding equation, point the mouse to the graph icon at the left of the equation and press the left mouse button. Answer (1 of 7): In terms of x by implicit diffrentiation (dv/dx)=(pi/3) ((r^2) (dh/dx) + (h) (2r) (dr/dx)) (dv/dx)=((pi r^2)/3) (dh/dx) + (2hr) (dr/dx)). Related Rates Ex 1: Related Rates: Determine the Rate …. 5) l Logarithmic Differentiation (3. Functions and Limits, continuity (Ch 1) Rate of change at an instant…. It can also graph conic sections, arbitrary inequalities or. Note: Creation of this applet was inspired by a related-rates problem taken from Section 3. Equation 1: related rates cone problem pt. ) Differentiating term by term, we find the most difficulty in the first term. ONLY label things that are constant. Topics in Calculus Name_____ Date_____ Period____ ©Z O2g021 e4T aK ruutqaM XS yoAf 0txw HamrBea ELvL PCT. Just so you know, related rates is actually the Application of Implicit Differentiation by using Chain Rule in the form of dy/dx = dy/du * du/dx. The rules of differentiation produce an equation relating the rates …. Click the "Close" button in the RelatedRates window to terminate the Maplet. This course introduces you to the concept of differential calculus and the various ways to calculate rates …. In “related rates” application problems, we often assume that all variables are Implicit Differentiation Formula” (IDF for short): If F(x,y)=0 defines a differentiable relation of x and y, then So, to calculate ∂F/∂x or ∂F/∂x, calculate dF/dx or dF/dx. Computing Input interpretation: differentiate x^3 + y^3 = 4 with respect to x . That being said, this is a scenario where most teachers would be for it and accept its usage. (3) Find the derivative of √ (xy) = e x - y Solution. 95) go > The study guide for Worldwide Differential …. Visual representation of concepts. Calculus: Early Transcendentals (2nd Edition) answers to Chapter 3 - Derivatives - 3. Module 28 - Activities for Calculus Using the TI-83. Implicit Differentiation Notes and Examples. The implicit differentiation calculator will find the first and second derivatives of an implicit …. Derivatives and the Shape of a Graph: Concavity and Points of Inflection. An Implicit Home Slope Newton's Method Related Rates Extrema Optimization Mathematics of Finance Economics Physics Solved Examples Word Problems use a graphing utility or an applicable calculator …. Example 4: A 50-ft ladder is placed against a building. , a problem that requires implicit differentiation…. Students will use implicit differentiation to solve a real-world related rate problem. Specifically for the AP® Calculus BC exam, this unit builds an understanding of straight-line motion to solve problems in which particles are moving along curves in the plane. Review for the Common Exam: MATH 151 Exam 1 Review Problems 10-13 Implicit differentiation and physics applications of derivatives…. In the list of Related Rates Problems which follows, most problems are average and a few are somewhat challenging. How to Use the Implicit Differentiation Calculator? The procedure to use the implicit Differentiation calculator is as follows: Step 1: Enter the equation in a given input field. The derivative of a given function y=f(x) y = f ( x) measures the instantaneous rate of change of the output variable with respect to the input variable. 264 » 20 MB) The derivative as rate of change. (7) Find the derivatives of the following. We help you handle and prevent agitated behavior. Some relationships cannot be represented by an explicit function. Connections to the Study Design: AOS 3 - Calculus. Download or read online full book title Developing Understanding Of The Chain Rule Implicit Differentiation And Related Rates …. Apply the derivative to calculate rates …. (a) We can answer this question two ways: using "common sense" or related rates. Draw a sketch if it is possible 3. Author: Haley Paige Jeppson Publisher: ISBN: Release Date: 2019 Size: 37. AP Calculus AB Course Curriculum. 2 Derivatives of Inverse Functions. derivatives, and implicit differentiation Me during related rates,. Implicit Differentiation Related Rates One of the applications of mathematical modeling with calculus involves related rates word problems. Find derivatives of radical functions Also consider: • Power rule II Related Rates 3. 4: Related Rates (preprinted) Chapter 3. 5 Derivatives and the Shape of a Graph. Related Rates 1: (dA)/dt = 2 \pi r (dr)/dt  Worksheet #35: W s #35 Solutions: 1-6, 7-10, 12 review: Related Rates 2: dz/dt = x dx/dt + y dy/dt Worksheet #36: Implicit Differentiation; Implicit Differentiation – Basic Idea and Examples ; Implicit Differentiation …. Limits: An Intuitive Approach - Answers. So the total rate of horiztonal displacement is 6m/s. Sketching Graphs 2: anti-derivatives. We use implicit differentiation to differentiate an implicitly defined function. Example 1: Find if x 2 y 3 − xy = 10. Strategy 1: Use implicit differentiation directly on the given equation. 11: Implicit Differentiation and Related Rates is shared under a CC BY 3. The topics below are both AB and BC topics. This can be done through the use of a financial calculator, software, an online calculator, or present value tables. In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. Differentials and Newton's method. Implicit differentiation will allow us to find an equation that. Learn to solve different kinds of related rates problems in Calculus. The derivate of a function at a chosen input value. A free online 2D graphing calculator (plotter), or curve calculator, that can plot piecewise, linear, quadratic, cubic, quartic, polynomial, trigonometric, hyperbolic, exponential, logarithmic, inverse functions given in different forms: explicit, implicit, polar, and parametric. Differentiating x to the power of something. Below you will find all homework assignments (and answers) for Calculus 1. {"results":"\u003cdiv class='col-xs-12 search-result-item thumbnail-card col-lg-6 col-sm-6' data-id='5439' data-item-type='CollectionItemFolder' data-type. We have seen how implicit differentiation can be used to find derivatives of implicit relations. Many (not all!) related rates problems present a quantity …. Download Vui lòng tải xuống để xem tài liệu đầy đủ. With an explicit function, given an x value, we have an explicit formula for computing the corresponding y value. Compute and interpret limits of functions using analytic and other methods, including L'Hospital's Rule. 2, 6 Important Example 23 Ex 5. How do you calculate the yearly inflation rate?. Notice that volume is a function of time because we’re looking at how volume changes over time (or the rate …. Resource Allocation: Implicit Differentiation; Related Rates; Business Applications: Social Sciences. Simply saying, it’s just the SLOPE of. Calculus is difficult part of mathematics and it. The idea behind linearization or local linear approximation is to find a value of the function at the given point and evaluate the derivative …. For most homework, a calculator will not be needed. Step by Step Implicit Differentiation Slope of Inverse Function All in one Rate Explorer Differentiability of piecewise-defined function Absolute and Percent Change Differentials APPS: Max Volume of Folded Box APPS: Min Distance Point to Function f(x) APPS: Related Rates …. Business and Industry Applications. Take help of free calculator to get Implicit Differentiation …. As your next step, simply differentiate the y terms the same way as you differentiated the x terms. cost, strength, amount of material used in a building, profit, loss, etc. Using the derivative to calculate the slope of a tangent at any point on a function. Calculate derivatives of hyperbolic functions. I know that y=3/4 from substituting xy=3 with x=-4, but I do not. Now differentiate with respect to x x. Implicit Differentiation and Related Rates In our work up until now, the functions we needed to differentiate were either given explicitly, such as y = x2 +ex, y = x 2 + e x, or it was possible to get an explicit formula for them, such as solving y3 − 3x2 = r y 3 − 3 x 2 = r to get y = 3√5+3x2. Related Rates are problems that connect rate …. In this section we are going to look at an application of implicit differentiation. Free Response: A calculator may not be used. Here we study several examples of related quantities that are changing with respect to time and we look at how to calculate one rate of change given another rate …. 9: Lecture 17: Related Rates ROTC Long Weekend Patrick's Videos: Logarithmic Differentiation Examples 1 2 3 Paul's Notes: Inverse Functions; 8: Mon 10/11: 3. High School Math Solutions – Derivative Calculator…. Rates of Change of Rectangle 3-8-21. Typically related rates problems will follow a similar pattern. The top of a ladder slides down a vertical wall at a rate of 0. Answer (1 of 9): To calculate the derivative of anything, you need to specify the variable that is changing. Practice: Analyzing related rates problems: expressions.