Question

d/dx integral e^t^2 dt from 1 to x^3

Please help. I think I'm supposed to use substitution for the x^3 and then apply the chain rule but I'm not sure how to do that.

Answer 1

The chain rule says that df/dx = df/du * du/dx. So, you have

e^(x^3)^2 (3x^2)
= 3x^2 e^(x^6)

now, technically, you have to subtract f(u) at the lower limit, but since d1/dx = 0, it just goes away.

wikipedia has a good article on this.