y=5x csc x Did I differentiate this correctly
5x-cscxcotx+cscx 5 I used the product rule
My second question is
y=-cscx-sin(x)
There should only be two terms when you use the product rule - not three. I suspect you mean $\displaystyle -5x \csc(x)\cot(x) + 5\csc(x)$ which is the correct.
Spoiler:
edit: I put the original second question in a spoiler since the OP edited it out
For your (new) second equation you can take the derivatives separately. $\displaystyle y = -\csc(x) - \sin(x)$
If you don't know the derivative of -csc(x) then you can write it as $\displaystyle -(\sin(x))^{-1}$ and use the chain rule.
Is your question $\displaystyle y = -\csc(x) \times - \sin(x)$ or $\displaystyle y = -\csc(x) - \sin(x)$ -- the latter is subtraction.
Since you've used the product rule I suspect it's the former. If so use the fact that $\displaystyle \sin(x)\csc(x) = 1$
That can be simplified:$\displaystyle \csc(x)\cos(x)-\cot(x)\csc(x)\sin(x)$
$\displaystyle \csc(x)\cos(x) - \cot(x)\csc(x)\sin(x) = \dfrac{\cos(x)}{\sin(x)} - \dfrac{\cos(x)\sin(x)}{\sin(x)\sin(x)} = 0$
-----------------------------------------------
edit: Please tidy your work up
-csc(x)-cos(x)+cot(x)csc(x)-sin(x) =$\displaystyle -\csc(x)-\cos(x)+\cot(x)\csc(x) - \sin(x)$ which clearly isn't right.
If you must use plain text then put it as -csc(x)*-cos(x)+cot(x)csc(x)*-sin(x) so we know you're multiplying by a negative number rather than subtracting.