Explanation Given: The function, y = 1 + 4 x 3 . Concept Used: The composition function f ∘ g can be found by replacing x by g ( x ) in the function f ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Derivative of any constant C is zero, that is, d d x ( C ) = 0 Exponent rule: a n = a 1 / n Calculation: In order to express the given function y = 1 + 4 x 3 as the composition of inner function u = g ( x ) and the outer function y = f ( u ) , observe that the inner function can be taken as u = g ( x ) = 1 + 4 x and outer function as y = f ( u ) = u 3 , because the composition of these functions gives y = f ( u ) = u 3 = 1 + 4 x 3 Thus, theinner function is u = g ( x ) = 1 + 4 x and y = f ( u ) = u 3

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.5, Problem 1E

To determine

To write thefunction y=1+4x3 as the composition of inner function u=g(x) and the outer function y=f(u) . And find the derivative dydx .

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Chapter 3.4, Problem 63E

Chapter 3.5, Problem 2E

Chapter 3 Solutions

Biocalculus

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