Question

What is the derivative of `f(x)=ln(secx)`?

Answer 1

`tan(x)`

Explanation:

We can use the chain rule here and substitute the inside of the ln function as u. So:

`ln(u), u=sec(x)`

We know the derivative of a ln function is in the form of `(u')/u`. So we need to find the derivative of `sec(x)`. This is a trig identity and so `(d(u))/dx=(d(sec(x)))/dx=sec(x)tan(x)=u'`

Putting this into our equation for the derivative of an ln function we get:

`(u')/u=(sec(x)tan(x))/sec(x)=tan(x)`