Consider the function .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the function

y=x\,e^{x^{2}}\cos 2x

. (a) Obtain

\dfrac{dy}{dx}

and simplify your result as far as possible. (b) Hence find the value of

\dfrac{dy}{dx}

x=0

. (c) Verify that

\dfrac{dy}{dx}

is an even function of

x

. (Show your working clearly.)

Related theory

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

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