Question

What is the derivative of e^x^2? and the second derivative if you can include as well. im not sure what the rule is. is it 2xe^x^2 for the first one? for the second one is it 2e^x^2 + 4x^2(e^x^2?

Answer 1

Thats correct for first derivative ( use the chain rule)

For the second derivative you use product rule and the chain rule

= 2x * 2x e^(x^2)  + 2 e^(x^2)
=  4x^2 e^(x^2) + 2e^(x^2)

you are right