I'm trying to find the derivative of:
$$y= \frac{x \sin(x)}{1+\cos(x)}$$
I've tried but I can't achieve the simplified form -
Here's my try-
$$y' = \left(\frac{x \sin(x)}{1+\cos(x)}\right)'$$
$$y' = \frac{x\sin^2(x) + (\cos(x)+1 )(\sin(x)+x\cos(x))}{(\cos(x)+1)^2}$$
I'm pretty sure the above is correct that is why I didn't show the steps in between ... but I can't simplify it until -
$$\frac{x+\sin(x)}{1+\cos(x)}$$
Which concept or formula am I missing out from in order to simplify it further? Or what should I do next? Thanks!