Question

derivative of csc x derivative of csc x @Mathematics

Answer 1

the answer is -csc(x)cot(x). I'll provide the steps in a second, wanna make it look neat.

Answer 2

\[\csc(x)=1/\sin(x)\]
same as
\[\sin(x)^-1\]
take the derivative
=\[-\sin^-2(\cos(x))\]
or
\[-\cos(x)/\sin^2(x)\]
split it up,
\[-1/\sin(x)*(\cos(x))/(\sin(x))\]
which leads us to

\[-\csc(x)*\cot(x)\]

Answer 3

There are a couple other ways you can prove it, that's just the simplest.