Question

What is the derivative of `5^x`?

Answer 1

`5^xln5`

Explanation:

Given: `d/dx(5^x)`.

Apply the general formula that `d/dx(a^x)=a^xlna \ "for" \ ainRR`.

`:.d/dx(5^x)=5^xln5`

Answer 2

`5^xln5`

Explanation:

`"let "y=5^x`

`"differentiate "color(blue)"implicitly with respect to x"`

`"take ln (natural log) of both sides"`

`lny=ln5^x=xln5`

`rArr1/ydy/dx=ln5`

`rArrdy/dx=yln5=5^xln5`