As the question prior to this one, differentiate cot^2(sin(theta))

Question

hartnn · Answer

whats your attempt ?

anonymous · Answer

All right.
So another chain rule.
2cot(sinx)[-csc^2(sinx)](cosx)  
I'm hoping that's right!

hartnn · Answer

that is correct :) 
just simplify it, -2...
and i also assume you mean theta (instead of x)

hartnn · Answer

oh, and this one can also be further simplified.

anonymous · Answer

Yes, sorry.
Yeah, I know. . I'm thinking either change the cot to cos/sin or the -csc^2 to 1/sin^2.
Is that legal?

hartnn · Answer

both are legal steps, if you convert everything to sin and cos, you'll be able to see the simplfication step.

anonymous · Answer

Whew, okay. But say I were to change the cot into cos/sin. since it's cot(sinTheta) it will be simplified to just cos, correct? Or is that not allowed since the "sinTheta" is an argumentation

hartnn · Answer

ohh.... irealised that now, the arguments are different(theta and sin theta), so no, they can be combined.
and you need to leave the answer as 
-2cot(sinx)csc^2(sinx)(cosx)

hartnn · Answer

**they cannot be combined

anonymous · Answer

aw, lame.  All righty