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

1 Answer
Jan 3, 2017

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)