Question

How do you find the derivative of `f(x) = (1/x)^x`?

Answer 1

`(dy)/(dx)=-x^{-x}(1+log_e x)`

Explanation:

`y = x^{-x}->log_ey=-x log_e x`
`dy/(y) = -dx log_e x-x/x dx = -(1+log_e x)dx`
then
`(dy)/(dx)=-y(1+log_e x)=-x^{-x}(1+log_e x)`