1. RE: Please differentiate this function.

cscθ(θ+cotθ)
cscθd/dθ(θ+cotθ)+(θ+cotθ)d/dθ(cscθ)
= cscθ(1-csc²θ)+(θ+cotθ)(-cscθcotθ)
But I'm having trouble simplifying from there. Thanks for any help!

2. Originally Posted by biozeta
cscθ(θ+cotθ)
cscθd/dθ(θ+cotθ)+(θ+cotθ)d/dθ(cscθ)
= cscθ(1-csc²θ)+(θ+cotθ)(-cscθcotθ)
But I'm having trouble simplifying from there. Thanks for any help!
$\csc{x}(1-\csc^2{x}) + (x+\cot{x})(-\csc{x}\cot{x})$

$\csc{x}(-\cot^2{x}) - x\csc{x}\cot{x} - \csc{x}\cot^2{x}$

$- x\csc{x}\cot{x} - 2\csc{x}\cot^2{x}$

$-\csc{x}\cot{x}(x + 2\cot{x})$

3. Originally Posted by biozeta
cscθ(θ+cotθ)
cscθd/dθ(θ+cotθ)+(θ+cotθ)d/dθ(cscθ)
= cscθ(1-csc²θ)+(θ+cotθ)(-cscθcotθ)
But I'm having trouble simplifying from there. Thanks for any help!

For being in Calculus the simplification of this should be trivial.

First, check to see if you have any identities. The pythagorean identity comes in handy A LOT in the simplification of these problems, but not this one necessarily.

Second, if the first fails to simplify anything move on to brute force your way through the problem via the distributive property. Once that's done, do you see any identities?

If no, then write your expanded solution as simplification, by definition, is done after those two steps.

EDIT:

Disregard me, I see someone posted the solution. So much for making the kid work for the answer :/

4. I got defensive when I saw the first line, but I gave your post a chance, and there were actually good problem-solving strategies. Thanks for helping!