Question

derivative of y=ln square root (1+sinx/1-sinx)

Answer 1

ok let \[u = \frac{ 1+\sin(x) }{ 1-\sin(x) }\]

Answer 2

use the Quotient rule\[\frac{ vdu-udv }{ v^2 }\]

Answer 3

Better be specific though...
\[\huge \frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\]

Answer 4

\[\frac{ (1-\sin(x))(\cos(x))-(1+\sin(x))(\cos(x)) }{ (1-\sin(x))^2 }\]

Answer 5

simplify the above expression

Answer 6

\[y =\frac{ 1 }{ 2 }\ln(u)\]

Answer 7

\[\frac{ dy }{ du }=\frac{ 1 }{ 2 }\frac{ 1 }{ u }\]

Answer 8

apply the chain rule

Answer 9

\[\frac{ dy }{ dx }=\frac{ dy }{ du}\frac{ du }{ dx }\]

Answer 10

@mathsmind
Something's not quite right... I think it should be
\[\large\frac{ (1-\sin(x))(\cos(x))-(1+\sin(x))(-\cos(x)) }{ (1-\sin(x))^2 }\]

Answer 11

yes the minus sign i deleted by mistake i just noticed

Answer 12

final answer is

Answer 13

\[\frac{ 1 }{ 2 }\frac{ \ln(\frac{ \cos(x) }{ 1-\sin(x) }+\frac{ (1+\sin(x))\cos(x) }{ (1-\sin(x))^2 }) }{ \sqrt{\frac{ 1+\sin(x) }{ 1-\sin(x) }} }\]

Answer 14

recall that \[\frac{ d }{ dx }\sin(x) = \cos(x)\]

Answer 15

A bit hard to read, @mathsmind
\[\huge \frac{ 1 }{ 2 }\frac{ \ln(\frac{ \cos(x) }{ 1-\sin(x) }+\frac{ (1+\sin(x))\cos(x) }{ (1-\sin(x))^2 }) }{ \sqrt{\frac{ 1+\sin(x) }{ 1-\sin(x) }} }\]

Answer 16

\[\frac{ d }{ dx}(1+\sin(x))=\cos(x)\]

Answer 17

change the resolution of the desktop or use opera browser

Answer 18

or just place \large or \huge before the entire thingy... :)

Answer 19

hehehe whatever

Answer 20

You couldn't be bothered to type an extra five characters? -.-

Answer 21

i am trying to get used to latex, so all my mind is focusing on coding

Answer 22

i need to memorize the user manual better

Answer 23

your resolution is too low that's why you are getting big fonts, at least set windows to small fonts

Answer 24

from the control pannel

Answer 25

Too much trouble :D

Answer 26

hehehe ok

Answer 27

i can see the full equation

Answer 28

acids taste sour and bases taste bitter

Answer 29

Where does this come from? 0.o

Answer 30

how did this post come into mathematics? errrr