Question

differentiate x^x with respect to x log x

Answer 1

Let y= x^x
ln y = x ln x
differentiate with respect to x ln x
d/d(x ln x) (y) = d/d(x ln x) ( x ln x)
dy/ d(x ln x) = 1


find dy:
ln y = x ln x
(1/y) dy = ln x + 1
dy = y (ln x + 1)
dy = x^x (ln x +1)

d(x ln x) = ln x + 1
dy/d(x ln x) = x^x (ln x +1) / (ln x +1) = x^x