Question

what is the derivative of y=4e^3x^2

Answer 1

ok, with this problem you need to know the product rule

Product rule:
F'S+FS'

F=4
F'=0
S=e^(3x^2)
S'=6x*e^(3x^2) (FYI, whenever you e^(a number) is always e^(a number), in other words, when you derive base e to a power of something, it is always the same.
derive of e^2 is e^2. always stay the same.

However, e^(3x^2) = 6xe^(3x^2)
^
notice how i derive the exponent and put it in front of e and the expo still stays the same.


now to put everything together.

(0)(e^(3x^2) + (4)(6xe^(3x^2) = your final answer
0 + 24xe^(3x^2)