Question

What is the derivative of `5^x`?

Answer 1

The derivative is `dy/dx=5^xln(5)`

Explanation:

Let `y=5^x`

Take natural log of each side

`lny=ln5^x=xln5`

Take the derivative of each side with respect to `x`

`1/y dy/dx=ln(5)`

`dy/dx=yln(5)`

Substitute `y`

`dy/dx=5^xln(5)`