Question

Let f(x)=4lnIsec(x)+tan(x)I find f"(x)

Answer 1

For ln(sec(x)) you need to do chain rule.
remember that \[\frac{d}{dx}ln(f(x))=\frac{1}{f(x)}*f'(x)\]
For the derivative for sec(x), you should note that sec(x) = 1/cos(x) whereupon you can do quotient rule
\[\frac{d}{dx}\frac{u}{v}=\frac{uv'+u'v}{v^2}\]
Similarly with tan(x) = sin(x)/cos(x) you can apply quotient rule here again.

The second derivative isn't much more strenuous.