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

q(x)=\sec\!\bigl(\sqrt{3x^{2}+1}\bigr)

. (a) Derive an expression for

q'(x)

in its simplest form. (b) Evaluate

q'(2)

, expressing your answer exactly. (c) Use the result from part (a) to explain whether

q

is increasing or decreasing at

x=2

Related theory

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

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