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Differentiate the following w.r.t. x: cos x by log x

9. Differentiate the following w.r.t. x: 

\frac{\cos x }{\log x} , x > 0 

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Given function is
f(x)=\frac{\cos x }{\log x}
We differentiate with the help of Quotient rule
f^{'}(x)=\frac{\frac{d(\cos x)}{dx}.\log x-\cos x.\frac{(\log x)}{dx} }{(\log x)^2 }
             =\frac{(-\sin x).\log x-\cos x.\frac{1}{x} }{(\log x)^2 } = \frac{-(x\sin x\log x+\cos x)}{x(\log x)^2}
Therefore, the answer is \frac{-(x\sin x\log x+\cos x)}{x(\log x)^2}

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