The function is defined by .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The function

y

is defined by

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

. (i) Obtain

\dfrac{dy}{dx}

. (ii) Find

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

. (iii) Evaluate

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

x=0

. (Give the exact value.)

Related theory

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

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