Use logarthmjc differentiation to find the derivative of the function y=x^sin (x)

dy/dx = x^sin (x) * (sin (x) / x + cos (x) * lnx)

Step-by-step explanation:

∵ y = x^sin (x)

∴㏑y = ㏑ (x^sin (x)) = sinx * ㏑x - - - by differentiating both sides with respect to x

(1/y) * dy/dx = sin (x) / x + cos (x) lnx

dy/dx = x^sin (x) * (sin (x) / x + cos (x) * lnx)