The function

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

Problem

The function f(x)=ex+xf(x) = e^x + x, being differentiable and one-one, has a differentiable inverse f−1(x)f^{-1}(x). The value of ddx(f−1)\frac{d}{dx}(f^{-1}) at the point f(log⁡2)f(\log 2) is (1) 1ln⁡2\frac{1}{\ln 2} (2) 13\frac{1}{3} (3) 14\frac{1}{4} (4) None of these

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