Because there is no X X derivative formula in the derivative formula of the basic function, it needs to be transformed.

Logarithm of both sides

lny=lnx^x

lny=xlnx

Because y is a function of x, both sides take the derivative of x.

On the left, because y is a function of x, y'/y can be obtained according to the derivative of the composite function.

Derivation of x on the right =x'*lnx

X*(lnx)', get lnx.

x/x

y'/y=lnx

x/x

y'=y*(lnx

1)

Because y = x x, it is substituted into the above formula.

derivation

y'=x^x*(lnx

1)