Question

How do you find the derivative of `3^(x^2-2)`?

Answer 1

`ln 9 \ x \ 3^(x^2-2)`

Explanation:

let `y = 3^(x^2-2)`

so `ln y = ln (3^(x^2-2)) = (x^2 - 2) ln 3`

`\implies 1/y y' = 2x ln 3`

`y' = 2x ln 3 * y = 2 \ ln 3 \ x \ 3^(x^2-2)`

`= ln 9 \ x \ 3^(x^2-2)`