Evaluate
-\left(\sin(\frac{x}{2})\sin(x\cos(x))+\cos(\frac{x}{2})\cos(x\cos(x))\right)
Differentiate w.r.t. x
\frac{2\sin(\frac{x\left(2\cos(x)-1\right)}{2})\left(-x\sin(x)+\cos(x)\right)+\sin(\frac{x\left(-2\cos(x)+1\right)}{2})}{2}
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