derivative of this equation?

[raven2k7]

hi, I am pretty much stuck at this point trying to figure out how they got this answer *-cosecx* I have uploaded the question and my working. maybe I am using the wrong steps. would like if someone could explain to me how it's done. thanks appreciated.

files are attached

 

[Dr.Peterson]

hi, I am pretty much stuck at this point trying to figure out how they got this answer *-cosecx* I have uploaded the question and my working. maybe I am using the wrong steps. would like if someone could explain to me how it's done. thanks appreciated.

Your second and third factors are wrong; can you show details on how you got them?

I'd simplify the function before differentiating, using properties of logs. It makes the work a lot easier and safer.

 

[raven2k7]

Since it was recommended that the OP goes through post #3, which is not valid at all I will show the 1st few steps.

[MATH]f(x) = \ln \sqrt {\dfrac{1+cosx}{1-cosx}} = \dfrac{1}{2}\ln(\dfrac{1+cosx}{1-cosx})=\dfrac{1}{2}[\ln(1+cosx)-\ln(1-cosx)][/MATH]
Now take the derivative of both sides,

Wow! thank god u came or i would have been greatly misguided. ok . i am going to try and take the derivative right now

 

[raven2k7]

Since it was recommended that the OP goes through post #3, which is not valid at all I will show the 1st few steps.

[MATH]f(x) = \ln \sqrt {\dfrac{1+cosx}{1-cosx}} = \dfrac{1}{2}\ln(\dfrac{1+cosx}{1-cosx})=\dfrac{1}{2}[\ln(1+cosx)-\ln(1-cosx)][/MATH]
Now take the derivative of both sides,

 

[Dr.Peterson]

@raven2k7
This is basically correct. On the first line, you omitted parentheses that appear on the next line; and you keep writing f(x) for what is really f'(x). It's important to distinguish the original function from its derivative.