Suppose and are differentiable and invertible with , ,

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Suppose ff and gg are differentiable and invertible with f(2)=5f(2)=5, f′(2)=−4f'(2)=-4, g(3)=5g(3)=5, and g′(3)=2g'(3)=2. Let p(x)=f−1(x) g−1(x)p(x)=f^{-1}(x)\,g^{-1}(x). Determine p′(5)p'(5). (a) −34-\dfrac34 (b) −18-\dfrac18 (c) 14\dfrac14 (d) 54\dfrac54

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