Question

What is the derivative of `ln(secx)`?

Answer 1

We can use the chain rule here!

First, let's rename `u=secx` and, consequently, `ln(u)` as our objective function.

Now, remembering the chain rule statement:

`(dy)/(dx)=(dy)/(du)(du)/(dx)`

Let's do it by parts:

`(dy)/(du)=1/u`

and

`(du)/(dx)=1*secxtanx`

Following the chain rule statement, we can aggregate them, now:

`(dy)/(dx)=1/u*secxtanx=(cancel(secx)tanx)/cancelsecx=color(green)tanx`