Question

What is the derivative of `5^(x/6)`?

Answer 1

`=((log 5)/6)5^(x/6)`

Explanation:

Use `a^(kx)=e^(x k log a)` and `(e^(bx))'=be^(bx)`.

`(5^(x/6))'`

`=(e^(((log 5)/6)x))'`

`=((log 5)/6)(e^(((log 5)/6)x))`

`=((log 5)/6)5^(x/6)`