Question

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

Answer 1

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)`