Solve cospi/x+cos3pi/x+cos5pi/x+cos7pi/x=

$$\cos \frac { \pi } { x } + \cos \frac { 3 \pi } { x } + \cos \frac { 5 \pi } { x } + \cos \frac { 7 \pi } { x } =$$

Evaluate

$$2\cos(\frac{\pi }{x})\left(\cos(\frac{2\pi }{x})+\cos(\frac{6\pi }{x})\right)$$

Differentiate w.r.t. x

$$\frac{\pi \sin(\frac{\pi }{x})\left(576\left(\cos(\frac{\pi }{x})\right)^{2}\left(\sin(\frac{\pi }{x})\right)^{4}-1040\left(\sin(\frac{\pi }{x})\right)^{2}\left(\cos(\frac{\pi }{x})\right)^{4}+160\left(\cos(\frac{\pi }{x})\right)^{6}-16\left(\sin(\frac{\pi }{x})\right)^{6}+8\left(\sin(\frac{\pi }{x})\right)^{4}+124\left(\cos(\frac{\pi }{x})\right)^{4}+48\left(\cos(\frac{\pi }{x})\right)^{2}-12\left(\sin(\frac{\pi }{x})\right)^{2}-47\left(\sin(\frac{2\pi }{x})\right)^{2}+4\right)}{4x^{2}}$$