Solve cos2alpha-cos3alpha-cos4alpha+cos5alpha

$$\cos 2 \alpha - \cos 3 \alpha - \cos 4 \alpha + \cos 5 \alpha$$

Evaluate

$$2\cos(\frac{7\alpha }{2})\left(\cos(\frac{3\alpha }{2})-\cos(\frac{\alpha }{2})\right)$$

Differentiate w.r.t. α

$$\frac{\sin(\alpha )\left(-20\left(\sin(\alpha )\right)^{4}-88\left(\cos(\alpha )\right)^{4}-64\cos(\alpha )\left(\sin(\alpha )\right)^{2}+64\left(\cos(\alpha )\right)^{3}+24\left(\cos(\alpha )\right)^{2}+53\left(\sin(2\alpha )\right)^{2}-12\left(\sin(\alpha )\right)^{2}-16\cos(\alpha )\right)}{4}$$