Question

How do you differentiate `y=x^(x-1)`?

Answer 1

`dy/dx= x^(x-1)*((x-1)/x+lnx)`

Explanation:

`y=x^(x-1)`

`lny = (x-1)*lnx`

`1/ydy/dx= (x-1)*1/x+lnx*1`

`dy/dx= y * ((x-1)*1/x+lnx)`

`dy/dx= x^(x-1)*((x-1)/x+lnx)`