What is the derivative of ##-csc(x)##?

##d/dx (-csc(x)) = -d/dx(csc(x))## Cosecant is the reciprocal of the sine function, so: ##-d/dx(1/sin(x))## You should know that the derivative of ##1/x = -1/x^2##. So by the : ##1/f(x) = -1/f(x)^2*d/dxf(x)##

Applying this here: ##-(-1/(sin^2(x))*d/dxsin(x))## ##= -(-1/(sin^2(x))*cos(x))## ## = cos(x)/(sin^2(x))d## This is already an answer but in most textbooks, you see it in a different form:

## 1/sin(x) * cos(x)/sin(x)## ##= csc(x)*cot(x)##

I hope this helped you in any way.