Let and let . Then is equal…

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

Problem

Let

f(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+\frac{x^5}{5}

and let

f^{-1}(x)=g(x)

. Then

g'''(0)

is equal to (A)

1

(B)

-1

(C)

2

(D)

-2

Related theory

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

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