I am having trouble finding trig derivatives using chain rule

[bblair3]

Homework Statement

cot^2(Cos$\theta$)

Homework Equations

chain rule
f prime (x) = f prime(g(x) * g prime (x)

The Attempt at a Solution

I am not sure if I am just inputting the wrong numbers into webassign or I am just missing and important trig derivative and just completely off of the boat here.

the answer I got the first time is:
-2 cot(cos$\theta$)*[-csc^2 (cos$\theta$) *-sin$\theta$)

thanks for any help you guys can give me

 

[process91]

Pretty close, you have an extra minus sign, that's all. How'd you arrive at that negative out in front?

 

[bblair3]

It looks like using the example I was looking at I distributed one extra negative sign

 

[bblair3]

I think there is one more step that I am lost on. I ended up getting 2 cos theta *cot(cos theta) *csc^2(-sin theta), which webassign did not like :( ahhhh

 

[process91]

You had the answer above already, with the exception of the extra minus sign.

To clarify, the question is:

What is the derivative of $\cot^2(\cos \theta)$?

You have already answered it above... how did you arrive at the second post?

 

[bblair3]

yes, the question you have is right.
I worked the problem by looking at an example video that comes with our online book.
the instructor in the video further broke down from the answer in the sample problem, which was cot^2(sin theta), which the answer is -2cos theta * cot(sin theta) *csc^2 (sin theta)

 

[bblair3]

oh i see what I did wrong! apparently the homework program did not like that I did not put a space between [-csc^2 and cos theta) wow here I was thinking I did not know what I was doing and it was just an input error, not a mathematical error! Got to love technology sometimes!

 

[process91]

Glad to hear you got it.

 

[bblair3]

thanks for the quick replies! sometimes it just takes a "fresh set of eyes" to say hey what are you doing there!