Differentiate and choose the correctly simplified form of .

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Differentiate

y = x^{2}e^{x}\sin x

and choose the correctly simplified form of

y'

. (a)

e^{x}\big[(2x+x^{2})\cos x + x^{2}\sin x\big]

(b)

e^{x}\big[2x\sin x + x^{2}\cos x\big]

(c)

e^{x}\big[(2x+x^{2})\sin x + x^{2}\cos x\big]

(d)

e^{x}\big[(2x+x^{2})\sin x + 2x\cos x\big]

Related theory

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

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