The derivative of the function

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

Problem

The derivative of the function, f(x)=cos⁡−1{113(2cos⁡x−3sin⁡x)}+sin⁡−1{113(2cos⁡x+3sin⁡x)}f(x) = \cos^{-1} \left\{ \frac{1}{\sqrt{13}} (2 \cos x - 3 \sin x) \right\} + \sin^{-1} \left\{ \frac{1}{\sqrt{13}} (2 \cos x + 3 \sin x) \right\} w.r.t. 1+x2\sqrt{1+x^2} at x=34x = \frac{3}{4} is (1) 32\frac{3}{2} (2) 52\frac{5}{2} (3) 103\frac{10}{3} (4) 0

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