Question

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

Answer 1

`(dy)/(dx)=2xe^(x^2)`

Explanation:

Right now, you have `y=e^(x^2)`

The derivative of `y=e^(f(x))` is `(dy)/(dx)=f'(x)e^(f(x))`

In this case, `f(x)=x^2`, and the derivative of `x^2=2x`

Therefore, `f'(x)=2x`, and `(dy)/(dx)=2xe^(x^2)`