How do I find the derivative of y= ln(1 + e^(2x)) ?

1 Answer
Jan 1, 2016

Using chain rule, which states that (dy)/(dx)=(dy)/(du)(du)/(dx)

Explanation:

We'll apply that logic for both the ln and the e^(2x), which demand chain rule to become differentiable.

Renaming u=1+e^(2x) we can differentiate the ln and by renaming v=2x we can differentiate the e^(2x).

(dy)/(dx)=1/u(2e^(2x))=(2e^(2x))/(1+e^(2x))