Question

Derivative need help !!

Answer 1

\[lntan(\frac{ x }{ 2 }+\frac{ \pi }{ 4 })\]

Answer 2

use the chain rule

Answer 3

how?

Answer 4

\[\huge \ln~\tan(\frac{ x }{ 2 } + \frac{ {\pi} }{ 2 })\]
\[\huge \frac{ 1 }{ \tan (x/2 + \pi/2) } * (\tan (x/2+\pi/2)'\]

Answer 5

yeh i did this

Answer 6

how to remove this angle ? of tan

Answer 7

the derivative is coming secx , and this angle is giving me problems

Answer 8

\[\huge (\tan x)' = \sec^2 x\]

Answer 9

yes bro i know this

Answer 10

pi/2 is a constant so it's derivative is 0

Answer 11

oh !!!

Answer 12

now i got it

Answer 13

(x/2)' = (2 - x(0)) / 4
= 1/2

Answer 14

so:
\[\huge \frac{ 1 }{ \tan(x/2+\pi/2) } * \sec^2(\frac{ 1 }{ 2 })x\]
right?

Answer 15

\[\huge \frac{ \sec^21/2x }{ \tan(x/2 + \pi/2) }\]

Answer 16

how to do this simplification ? o_o

Answer 17

so hard

Answer 18

oh you have to simplify it..uh

Answer 19

@Loser66 could you take it from here? i'm a bit exhausted... xD

Answer 20

Not sure :)

Answer 21

according to wolframalpha it becomes:
\[\tan(x/2) (-\sec^2(x/2))\]

Answer 22

to me, I will manipulate the tan a little bit
tan (x/2 +pi/4) =\(\large \dfrac{tan x/2 + tan pi/4}{1-tan x/2*tanpi/4}= \Large \frac{tan x/2 +1}{1-tan x/2}\)
now, put it in ln
\(ln \frac{tan x/2 +1}{1-tanx/2}=ln (tanx/2 +1) - ln (1-tan x/2)\)
It's quite easy to take derivative now.

Answer 23

Where did the \(\pi/4\) go?

Answer 24

tan45 = 1

Answer 25

or tan pi/4 = 1

Answer 26

\(\dfrac{d}{dx}\ln\left[\tan\left(\dfrac{x}{2}+\dfrac{\pi}{4}\right)\right] = \dfrac{1}{\tan\left(\dfrac{x}{2}+\dfrac{\pi}{4}\right)}\cdot\sec^{2}\left(\dfrac{x}{2}+\dfrac{\pi}{4}\right)\cdot\dfrac{1}{2}\)

You can't just through away \(\pi/4\) because you don't like it.

Answer 27

@tkhunny I am sorry, I don't get what you mean by "throw pi/4 away"

Answer 28

@Loser66 No, no. You're fine. It's the previous method shown here that seems to have done what I suggested.

Answer 29

:)

Answer 30

but how this is going to be simplified ? sec^2(1/2x)tan(x/2+π/2)

Answer 31

sec^2(1/2x)/tan(x/2+π/2

Answer 32

sorry it is sec^2(1/2x)tan(x/2+π/4)