Question

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

Answer 1

Answer:

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)