Hey! Have you tried to solve it this way?

y =x^{sin(x)}

y = exp(log(x^{sin(x)}))= e^{sinx*log(x)},

dy/dx = [sin(x)/x + ln(x)cos(x)]e^{sin(x)log(x)} = [sin(x)/x + ln(x)cos(x)]x^{sin(x)} .