f(x)=3ln[sec(x)+tan(x)]
f(x)=
I got (((3sec(x))(tan(x))^2)-(3(sec(x))^2)-(2(sec(x))^2)(tan(x))(sec(x)tan(x))+(-3(sec(x)tan(x)+(sec(x))^2)(-sec(x)tan(x)+(sec(x))^2)))/((sec(x)+tan(x))^2)
you're making your life WWWAAAYYYY too complicated. simplify intermediate steps before moving on
well, by definition, the derivative of ln|sec(x) + tan(x)| = sec(x), but let's pretend we didn't know that.
we have to use the chain rule:
f(x) = 3ln|sec(x) + tan(x)|
=> f ' (x) = 3[1/(sec(x) + tan(x)) * (sec(x)tan(x) + sec^2(x))]
.............= 3[{sec(x)tan(x) + sec^2(x)}/{sec(x) + tan(x)}]
.............= 3[sec(x){tan(x) + sec(x)}/{sec(x) + tan(x)}]
.............= 3sec(x)
=> f '' (x) = 3sec(x)tan(x)