how would i find the derivative of cos(x)-xcsc(x)?

Question

anonymous · Answer

find derivative of cosx, then use uv-vdu for xcscx to get derivative

anonymous · Answer

What is uv-vdu?

anonymous · Answer

integration by parts

anonymous · Answer

@dorky_nefty, if you know the derivative of $\cos x$, the first term is simple to differentiate.

For the second term, $-x\csc x$, you have to use the product rule.

Overall, you have
$$\begin{align*}\frac{d}{dx}\left(\cos x-x\csc x\right)&=\frac{d}{dx}\cos x-\frac{d}{dx}x\csc x\
&=\frac{d}{dx}\cos x-\left(\frac{d}{dx}[x]\csc x+x\frac{d}{dx}[\csc x]\right)\
\end{align*}$$

anonymous · Answer

looking at this answer above me.. seems wrong LOL

anonymous · Answer

Okay I think I know what I have to do now thanks :)

anonymous · Answer

You're welcome