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How do you differentiate #y=(e^(2x)+1)^3#?

1 Answer

Dec 10, 2016

You have to use the chain rule: #f(g(x))' = f'(g(x)) * g'(x)#

Explanation:

In this case #g(x) = e^(2x) + 1# , so we have:

#g'(x) = 2 e^(2x)#, again by the chain rule.

And #f'(e^(2x) + 1) = 3 (e^(2x) + 1)^2#.

Putting it all together we have:

#3 (e^(2x) + 1)^2 * 2 e^(2x) = 6 (e^(2x) + 1)^2 * e^(2x)#

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