Question

What is the derivative of `y=5^(-1/x)`?

Answer 1

`dy/dx = ln5/(x^2*5^(1/x))`

Explanation:

`y=5^(-1/x)`

`lny =-1/x*ln5 = -ln5 *x^(-1)`

`1/y dy/dx = ln5*x^(-2)`
(Implicit differentiation, standard differential and power rule)

`dy/dx = ln5*x^(-2) * y`

`=ln5*x^(-2) * 5^(-1/x)`

`=ln5/(x^2*5^(1/x))`