I have to take the AP Calculus AB test tomorrow, so anyone who can clarify this for me quickly would be much, much appreciated.
I understand that when I perform the chain rule with a derivative, such as d/dx (2x+1)^3, I must take the derivative, yielding 3(2x+1)^2, and then I must multiply by the derivative of the inside, d/dx (2x+1) = 2, yielding 2*3(2x+1)^2 -> 6(2x+1)^2.
However, I am confused on this when I am using something other than a simple binomial. If I must evaluate d/dx (e^2x), would the derivative simply be (e^2x), or would I multiply that by the derivative of the exponent (d/dx 2x = 2), making it 2*(e^2x) -> (2e^2x)?
If the latter is true and I must multiply by the derivative of the exponent, then what do I do when I must take the antiderivative of it? For example, if I am given ∫(e^2x)dx, would the answer be (1/2)(e^2x)+C ?
Please correct anything I am mistaken on. Thank you.