Differentiate the function w.r.t.x. : 
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nice question and also U try first.
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we have to differentiate the function, 
first of all, taking ‘ log ’ both sides ,
![logy=log\{xcosx-sinx)^x\}\\\\logy=xlog\{xcosx-sinx\}\\\\\frac{1}{y}\frac{dy}{dx}=\frac{d\{xlog(xcosx-sinx)\}}{dx}\\\\\frac{dy}{dx}=y\left[x\frac{d\{log(xcosx-sinx)\}}{dx}+log(xcosx-sinx)\frac{dx}{dx}\right]\\\\\frac{dy}{dx}=(xcosx-sinx)^x\left[x\frac{1}{(xcosx-sinx)}\{\frac{d(xcosx)}{dx}-\frac{d(sinx)}{dx}\}+log(xcosx-sinx)\right]\\\\\frac{dy}{dx}=(xcosx-sinx)^x\left[x\frac{(cosx-xsinx-cosx)}{(xcosx-sinx)}+log(xcosx-sinx)\right]\\\\\frac{dy}{dx}=(xcosx-sinx)^x\left[\frac{-x^2sinx}{(xcosx-sinx)}+log(xcosx-sinx)\right]](https://tex.z-dn.net/?f=logy%3Dlog%5C%7Bxcosx-sinx%29%5Ex%5C%7D%5C%5C%5C%5Clogy%3Dxlog%5C%7Bxcosx-sinx%5C%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7By%7D%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bd%5C%7Bxlog%28xcosx-sinx%29%5C%7D%7D%7Bdx%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3Dy%5Cleft%5Bx%5Cfrac%7Bd%5C%7Blog%28xcosx-sinx%29%5C%7D%7D%7Bdx%7D%2Blog%28xcosx-sinx%29%5Cfrac%7Bdx%7D%7Bdx%7D%5Cright%5D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28xcosx-sinx%29%5Ex%5Cleft%5Bx%5Cfrac%7B1%7D%7B%28xcosx-sinx%29%7D%5C%7B%5Cfrac%7Bd%28xcosx%29%7D%7Bdx%7D-%5Cfrac%7Bd%28sinx%29%7D%7Bdx%7D%5C%7D%2Blog%28xcosx-sinx%29%5Cright%5D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28xcosx-sinx%29%5Ex%5Cleft%5Bx%5Cfrac%7B%28cosx-xsinx-cosx%29%7D%7B%28xcosx-sinx%29%7D%2Blog%28xcosx-sinx%29%5Cright%5D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28xcosx-sinx%29%5Ex%5Cleft%5B%5Cfrac%7B-x%5E2sinx%7D%7B%28xcosx-sinx%29%7D%2Blog%28xcosx-sinx%29%5Cright%5D "logy=log\{xcosx-sinx)^x\}\\\\logy=xlog\{xcosx-sinx\}\\\\\frac{1}{y}\frac{dy}{dx}=\frac{d\{xlog(xcosx-sinx)\}}{dx}\\\\\frac{dy}{dx}=y\left[x\frac{d\{log(xcosx-sinx)\}}{dx}+log(xcosx-sinx)\frac{dx}{dx}\right]\\\\\frac{dy}{dx}=(xcosx-sinx)^x\left[x\frac{1}{(xcosx-sinx)}\{\frac{d(xcosx)}{dx}-\frac{d(sinx)}{dx}\}+log(xcosx-sinx)\right]\\\\\frac{dy}{dx}=(xcosx-sinx)^x\left[x\frac{(cosx-xsinx-cosx)}{(xcosx-sinx)}+log(xcosx-sinx)\right]\\\\\frac{dy}{dx}=(xcosx-sinx)^x\left[\frac{-x^2sinx}{(xcosx-sinx)}+log(xcosx-sinx)\right]")
first of all, taking ‘ log ’ both sides ,
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