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