The derivative of f(x)= ^ -1 ( 1 3 (2 x-3 x) )+ ^ -1 ( 1 3 (2 x+3 x) ) w.r.t

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

Problem

The derivative of f(x)=cos⁡−1(13(2cos⁡x−3sin⁡x))+{sin⁡−1(13(2cos⁡x+3sin⁡x))} w.r.t. 1+x2 at x=13 is ..... .\text{The derivative of } f(x)=\cos^{-1}\left(\frac{1}{\sqrt{3}}(2\cos x-3\sin x)\right)+\left\{\sin^{-1}\left(\frac{1}{\sqrt{3}}(2\cos x+3\sin x)\right)\right\}\text{ w.r.t. } \sqrt{1+x^2}\text{ at } x=\frac{1}{\sqrt{3}}\text{ is ..... .}

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