(a) State the rule for the derivative of the product of two differentiable functions.…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

(a) State the rule for the derivative of the product of two differentiable functions. (b) Let

f(x)=x\sin x

. Find

f'(x)

, showing each step clearly. (c) Explain briefly why the derivative obtained in part (b) naturally contains two separate terms.

Related theory

Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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