Let be defined as and

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

Problem

Let f:(0,∞)→(−∞,∞)f:(0,\infty)\to(-\infty,\infty) be defined as f(x)=ex+ln⁡xf(x)=e^x+\ln x and g=f−1g=f^{-1}, then (a) g′(e)=1−e(1+e)3g'(e)=\frac{1-e}{(1+e)^3} (b) g′′(e)=e−1(1+e)3g''(e)=\frac{e-1}{(1+e)^3} (c) g′(e)=e+1g'(e)=e+1 (d) g′(e)=1e+1g'(e)=\frac{1}{e+1}

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