Solve d/dxleft(sqrt{left(sin(x)-2sin(2x)right)^2+left(-2sin(x)right)^2}right)

$$\frac{d}{d x } \left( \sqrt{ { \left( \sin ( x ) -2 \sin ( 2x ) \right) }^{ 2 } + { \left(-2 \sin ( x ) \right) }^{ 2 } } \right)$$

Evaluate

$$\frac{\cos(x)sign(\sin(x))\left(16\left(\cos(x)\right)^{2}-8\cos(x)+5\right)+4\sin(x)|\sin(x)|\left(-4\cos(x)+1\right)}{\sqrt{16\left(\cos(x)\right)^{2}-8\cos(x)+5}}$$

Differentiate w.r.t. x

$$\frac{4\left(-128\sin(x)sign(\sin(x))\left(\cos(x)\right)^{4}+96\sin(x)sign(\sin(x))\left(\cos(x)\right)^{3}-64|\sin(x)|\left(\cos(x)\right)^{4}-56\sin(x)sign(\sin(x))\left(\cos(x)\right)^{2}+48|\sin(x)|\left(\cos(x)\right)^{3}+16|\sin(x)|\left(\sin(x)\right)^{2}-28|\sin(x)|\left(\cos(x)\right)^{2}+5\sin(2x)sign(\sin(x))+5\cos(x)|\sin(x)|\right)-|\sin(x)|\left(16\left(\cos(x)\right)^{2}-8\cos(x)+5\right)^{2}}{\left(16\left(\cos(x)\right)^{2}-8\cos(x)+5\right)^{\frac{3}{2}}}$$