Mathematics

Problem

The function

y

is defined by

y=e^{x^{2}}\,\cos\bigl(\sqrt{3x^{3}+2}\bigr)

. a. (i) Obtain

\dfrac{dy}{dx}

. b. (ii) Find

\dfrac{d^{2}y}{dx^{2}}

. c. (iii) Evaluate

\dfrac{d^{2}y}{dx^{2}}

x=0

. (Give the exact value.)