differentiate the following function with respect to x

x^(sin x)

y=x^sinx

^{taking log on both sides}

logy=sinx.logx

diff.w.r.to x using product rule of two function

(1/y)dy/dx=sinx.(1/x)+logx(cosx)

dy/dx=x^sinx[(sinx)/x +cosx logx]

Thanks & Regards

Rinkoo Gupta

askIITians Faculty