Consider the function .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Consider the function f(x)=(3x2+2x+1)5f(x)=\bigl(3x^{2}+2x+1\bigr)^{5}. (a) State the formula for the derivative of a composite function y=f(g(x))y=f\bigl(g(x)\bigr). (b) Obtain f′(x)f'(x) in simplified form without expanding the binomial. (c) Hence, calculate f′(0)f'(0), giving the exact value.

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