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Question

Find the derivative of f(x)=cos⁡(tan⁡−1(10ln⁡x))f\left(x\right)=\cos\left(\$$tan^{-1}$$\left(10\ln x\right)\right).

Accepted Answer

−10sin⁡(tan⁡−1(10ln⁡x))x(1+(10ln⁡x)2)-\frac{10\sin\left(\$$tan^{-1}$$\left(10\ln x\right)\right)}{x\left(1+\left(10\ln x\$$right)^2$$\right)}

Answer

csc⁡2(tan⁡−1(10ln⁡x))x(1−(10ln⁡x)2)\frac{\$$csc^{2^{}$$}\left(\$$tan^{-1}$$\left(10\ln x\right)\right)}{x\left(1-\left(10\ln x\$$right)^2$$\right)}

Answer

−csc⁡2(tan⁡−1(10ln⁡x))x(1−(10ln⁡x)2)-\frac{\$$csc^2$$\left(\$$tan^{-1}$$\left(10\ln x\right)\right)}{x\left(1-\left(10\ln x\$$right)^2$$\right)}

Answer

10sin⁡(tan⁡−1(10ln⁡x))x(1+(10ln⁡x)2)\frac{10\sin\left(\$$tan^{-1}$$\left(10\ln x\right)\right)}{x\left(1+\left(10\ln x\$$right)^2$$\right)}

Find the derivative of f(x)=cos(tan−1(10lnx))f\(\left\)(x\(\right\))=\(\cos\]\left\)(\(\tan\)^{-1}\(\left\)(10\(\ln\) x\(\right\))\(\right\)).