Can anyone differentiate this :
y=Ln(tg(x/2))

Question

Can anyone differentiate this : 
y=Ln(tg(x/2))

hartnn · Answer

tg is tangent function ?

anonymous · Answer

Yes

hartnn · Answer

do you know chain rule ?

anonymous · Answer

I know how to do this type of problems but I can't get the right answer and I don't know where I go wrong

hartnn · Answer

so sho me your attempt, maybe i will find the error in your work...

hartnn · Answer

you know derivates of ln x, tg x and x/2 , right ?

anonymous · Answer

(1/(2cos^2 x/2))/tg x/2

hartnn · Answer

did u mean, 
$\huge \dfrac{\dfrac{1}{2\cos^2(x/2)}}{\tan(x/2)}$

if yes, thats correct, just try to simplify a bit.

anonymous · Answer

Yes that's what I meant. And when I simplify it I get 1/(2sin x/2 * cos x/2)

anonymous · Answer

I don't know what to do from there on. None of the answers match.

hartnn · Answer

which is still correct
now use 
sin  2x = 2 sin x cos x

so, 
2sin x/2 * cos x/2 will be just sin x

and 1/sin x = cosec x
is cosec x in choices ?

hartnn · Answer

and did u get what i did ?

anonymous · Answer

Oh yes, you are right! I forgot to use that equation at the end. The answer is 1/sinx. Thanks!! :)

hartnn · Answer

welcome ^_^