Consider the function .

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

Problem

Consider the function

y = \bigl(\sin(2x^{2}+1)\bigr)^{5}

. (i) Find

\displaystyle \frac{dy}{dx}

and express your answer in simplified factored form. (ii) Hence evaluate

\displaystyle \frac{dy}{dx}

x = 0

. (iii) Verify that your simplified derivative from part (i) reduces correctly when

x=0

Related theory

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

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