Mathematics

Problem

Consider the function

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

. a. (a) Obtain

\dfrac{dy}{dx}

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

\dfrac{dy}{dx}

x=0

. c. (c) Verify that

\dfrac{dy}{dx}

is an even function of

x

. (Show your working clearly.)