Question

How do you find the derivative of `y=a^x`?

Answer 1

For `a > 0`.

If you haven't memorized `d/(dx)(a^x) = a^x lna`, then you use

`y=a^x = e^(ln(a^x)) = e^(xlna)` and differentiate using the chain rule to get:

`y' = e^(xlna) (lna) = a^x lna`