![]() At a particular time car A is \(10\) kilometres to the north of \(P\) and traveling at 80 km/hr, while car B is 15 kilometres to the east of \(P\) and traveling at 100 km/hr. When defining the derivative \(f^\) Car A is driving north along the first road, and car B is driving east along the second road. Implicit and Logarithmic Differentiation.Derivatives of Exponential & Logarithmic Functions Related rates problems are applied problems where we find the rate at which one quantity is changing by relating it to other quantities whose rates are known.Derivative Rules for Trigonometric Functions. ![]() Limits at Infinity, Infinite Limits and Asymptotes.Symmetry, Transformations and Compositions.Suppose they are related by the equation 3P2. Example: RelatedRates 1 Suppose P and Q are quantities that are changing over time, t. Open Educational Resources (OER) Support: Corrections and Suggestions Chapter 3: Applications of Derivatives 3.2: Related Rates Related Rates - Introduction 'Related rates' problems involve nding the rate of change of one quantity, based on the rate of change of a related quantity.If the problems involves more than two rates, the process is the same but you will need to be given more information to plug in. This new equation will relate the derivatives. Using the chain rule, differentiate both sides of the equation found in step 3 with respect to the independent variable. Likely the equation will be a simple linear function of the rate so just divide by everything else. Find an equation relating the variables introduced in step 1. Once the only unknown that remains is the rate you want to find then you can solve for that rate. Often you will reuse the equation that was differentiated to solve for the final variable. Compute the radius from this information. If the problem is meant to be harder then you might be given the diamter or the volume of the sphere. If the problem is meant to be easy then the radius will be given directly. The question should mention something about when to compute the rate of change. A 6ft man walks away from a street light that is 21 feet above the g. Write this rate in a form similar to $\frac$ is $r$, and you should be able to figure this out from the problem. This calculus video tutorial explains how to solve the shadow problem in related rates. ![]() For example, if we know how fast water is being pumped into a tank we can calculate. ![]() Read the problem and find a rate that is given. Related rates problems ask how two different derivatives are related. ![]()
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