Question

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

Answer 1

`d/(dx) 3^(x^2) =2xln3 *3^(x^2)`

Explanation:

Note that:

`3^(x^2) = (e^ln3)^(x^2)= e^(ln3x^2)`

Using the chain rule:

`d/(dx) 3^(x^2) = d/(dx) e^(ln3x^2) = e^(ln3x^2)*d/(dx) (ln3x^2) = 2ln3xe^(ln3x^2)=2ln3 x 3^(x^2)`