Question

Differentiate x to the power x from first principle?

Answer 1

given that

f(x)= y. f(x) = x^x

:. y=x^x

:. log(y)= log(x)^x

:. log(y)= x . log(x)

now differentiating both sides with respect to x

:. 1/y dy/dx = 1. log(x) + x . 1/x

dy/dx = [1+ log(x)] x^x.