The first derivative of the function with respect to at is

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

Problem

The first derivative of the function [cos⁡−1(sin⁡1+x2)+xx]\left[ \cos^{-1} \left( \sin \sqrt{\frac{1+x}{2}} \right) + x^x \right] with respect to xx at x=1x = 1 is (a) 3/43/4 (b) 0 (c) 1/21/2 (d) −1/2-1/2

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