Question

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

Answer 1

Assuming that the function ought to be `y= (e^(2x) + 1)^3`, use the chain rule twice.

Explanation:

`y= (e^(2x) + 1)^3`

`dy/dx= 3(e^(2x) + 1)^2 [d/dx(e^(2x) + 1)]`

`= 3(e^(2x) + 1)^2[e^(2x)d/dx(2x)]`

`= 3(e^(2x) + 1)^2e^(2x)2`

`= 6e^(2x)(e^(2x) + 1)^2`