Hi all just studying up for my exam :grumpy: im scared,(adsbygoogle = window.adsbygoogle || []).push({});

ive been going over some practice questions and im stuck with a couple and would like some better understanding of another.

first of all:

determine the derivatives of each of the following functions

(1) x^3 e^2x

with this i know that the answer is x^2(3+2x)e^2x. i got the answer right but even im not sure how, could someone explain to me the (3+2x) in the brackets, i dont understand it because i know d/dx e^x = e^x and d/dx e^f(x) = e^f(x) x f '(x).

(2) e^(x^2+1)^1/2

with this one i tried using the chain rule for (x^2+1)^1/2 to get the derivative, i got what i thought was the right answer but wasnt. what am i doing wrong here? am i using the right rule?

(3) (e^2x - 2e^x)^2

once again i tried the chain rule here ended up getting close to the answer but it all seemed to cancel each other out? i belive i got close to this one but iam missing something. once again am i using the right rule?

(4) e^x + e^-x / e^x - e^-x

i tried the quotient rule for this one but i pretty much ended up with the same but with (e^x - e^-x) on top with e^x + e^-x.

any help would be appreciated thanks guys

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# Derivatives of Exponentials

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