Whenever we are finding the derivative of a function, be it a composite function or not, we. One can ask whether the vehicles are getting closer or further apart and at what rate at the moment when the northbound vehicle is 3 miles north of the intersection and the westbound vehicle is 4 miles east of the intersection.īig idea: use chain rule to compute rate of change of distance between two vehicles. If the function y is a natural log of a function of y, then you use the log rule and the chain rule. Chain Rule Help The chain rule is similar to the product rule and the quotient rule, but it deals with differentiating compositions of functions. Chain Rule appears everywhere in the world of differential calculus. Show Solution For this problem each term will require a separate application of the Chain Rule and make sure you are careful with parenthesis in dealing with the root in the first term. The chain rule can be used to find whether they are getting closer or further apart.įor example, one can consider the kinematics problem where one vehicle is heading west toward an intersection at 80mph while another is heading north away from the intersection at 60mph. Sometimes separate terms will require different applications of the Chain Rule, or maybe only one of the terms will require the Chain Rule. The chain rule is a method to compute the derivative of the functional composition of two or more functions.
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