Question

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

Answer 1

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))`