Find the derivative of f(x)=xcos(x)f(x) = x^{\cos(x)}f(x)=xcos(x) for x>0x > 0x>0.
xcosx(−sinxlnx+cosxx)x^{\cos x} (-\sin x \ln x + \frac{\cos x}{x})xcosx(−sinxlnx+xcosx)
xcosx(sinxlnx+cosxx)x^{\cos x} (\sin x \ln x + \frac{\cos x}{x})xcosx(sinxlnx+xcosx)
cos(x)xcosx−1\cos(x) x^{\cos x - 1}cos(x)xcosx−1
xcosx(−sinxlnx−cosxx)x^{\cos x} (-\sin x \ln x - \frac{\cos x}{x})xcosx(−sinxlnx−xcosx)