Let for all real .

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

Problem

Let f(x)=(x2+1)3x ex2f(x)=(x^2+1)^{3x}\,e^{x^2} for all real xx. (a) Derive an explicit expression for f′(x)f'(x). All steps leading to the final simplified result must be shown. (b) Evaluate f′(0)f'(0). Show your numerical substitutions clearly.

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