Explain in one or two sentences why the derivative of cannot be obtained by simply…

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

Problem

Explain in one or two sentences why the derivative of

f(x)=x\sin x

cannot be obtained by simply multiplying

\dfrac{d}{dx}(x)

and

\dfrac{d}{dx}(\sin x)

Related theory

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

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