Differentiate the following. (a) y = sin(x4) (b) y = sin(x) Solution (a) If y = sin(x4), then the outer function is the sine function and the inner function is the power function, so the Chain Rule gives the following. d dy dx dx = dy dx (b) Note that sin(x) = (sin(x)) = = sin d dx outer function (sin(x)) 4 inner function (x4) evaluated at inner function (x4) evaluated derivative of outer at inner function function COS Here the outer function is the power function and the inner function is the sine function. So = 4. (sin(x))³ derivative of outer function evaluated at inner function derivative of inner function derivative of inner function
Differentiate the following. (a) y = sin(x4) (b) y = sin(x) Solution (a) If y = sin(x4), then the outer function is the sine function and the inner function is the power function, so the Chain Rule gives the following. d dy dx dx = dy dx (b) Note that sin(x) = (sin(x)) = = sin d dx outer function (sin(x)) 4 inner function (x4) evaluated at inner function (x4) evaluated derivative of outer at inner function function COS Here the outer function is the power function and the inner function is the sine function. So = 4. (sin(x))³ derivative of outer function evaluated at inner function derivative of inner function derivative of inner function
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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