Question

Let f(x)=4lnabsolutevalue(sec(x)+tan(x))

Answer 1

Oh this is a fun one :) lol

Answer 2

f'=secx

Answer 3

\[ \large f(x) = 4\ln\vert\sec(x) + \tan(x)\vert\]

Answer 4

this is a formula !!

Answer 5

Yah but he probably needs to do the work mah... -_-

Answer 6

4 sec x

Answer 7

He/she hasn't said what they want to do with it :)

Answer 8

Hmmmmm true :) Find f'(x)? What's up AJ? :D

Answer 9

Actually it gets even more fun it is find f"(x)

Answer 10

Are you allowed to use the shortcut that mahmit posted? Or do you need to show all the steps?
(This is a derivative that eventually you'll just memorize, that's why i ask)

Answer 11

it was obvious what he/she wanted !!

Answer 12

I need to show the steps unfortunately :(

Answer 13

lu)'=u'/u

Answer 14

4secxtanx+sec2x/secx+tanx=4secx

Answer 15

I thought that the derivative sec(x)tan(x) not sec(x)+tan(x) equaled sec(x)

Answer 16

(secx)'=secx(tanx)

Yes that is true, that's where we'll be heading after we find the first derivative.
The first derivative unfortunately will give us something rather sloppy, and we'll have to do a little work to simplify it down.