What is the derivative of ln(secx)?

1 Answer
May 25, 2015

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