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

Answer 1

Scarlett Allison

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

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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Answer 2

Emilia Aguilar

To differentiate ( y = (e^{2x} + 1)^3 ), you can use the chain rule.

First, differentiate the outer function ( u^3 ) with respect to ( u ), which gives ( 3u^2 ).

Then, differentiate the inner function ( e^{2x} + 1 ) with respect to ( x ), which is ( 2e^{2x} ).

Combine the results using the chain rule, so the final derivative is ( \frac{d}{dx} (e^{2x} + 1)^3 = 3(e^{2x} + 1)^2 \cdot 2e^{2x} ).

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Answer from HIX Tutor

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