Solve d/dx([e^2x*cos(sinx)]^5/[operatorname{cosesin(ln2x^2)]^9})

$$\frac { d } { d x } ( \frac { [ e ^ { 2 x } \cdot \cos ( \sin x ) ] ^ { 5 } } { [ \operatorname { cosesin } ( \ln 2 x ^ { 2 } ) ] ^ { 9 } } )$$

Evaluate

$$\frac{e^{10x}\left(\cos(\sin(x))\right)^{4}\left(-18\ln(2)x\cos(\sin(x))\cos(\ln(2)x^{2})-5\cos(x)\sin(\sin(x))\sin(\ln(2)x^{2})+10\cos(\sin(x))\sin(\ln(2)x^{2})\right)}{\left(\cos(e)\right)^{9}\left(\sin(\ln(2)x^{2})\right)^{10}}$$

Differentiate w.r.t. x

$$\frac{\left(\cos(\sin(x))\right)^{3}\left(40\left(\cos(x)\sin(\sin(x))\sin(\ln(2)x^{2})\right)^{2}-10\left(\cos(x)\cos(\sin(x))\sin(\ln(2)x^{2})\right)^{2}+72\left(\ln(2)x\cos(\sin(x))\sin(\ln(2)x^{2})\right)^{2}+720\left(\ln(2)x\cos(\sin(x))\cos(\ln(2)x^{2})\right)^{2}+200\left(\cos(\sin(x))\sin(\ln(2)x^{2})\right)^{2}+5\sin(x)\sin(2\sin(x))\left(\sin(\ln(2)x^{2})\right)^{2}-100\cos(x)\sin(2\sin(x))\left(\sin(\ln(2)x^{2})\right)^{2}+90\ln(2)x\cos(x)\sin(2\sin(x))\sin(2\ln(2)x^{2})-360\ln(2)x\left(\cos(\sin(x))\right)^{2}\sin(2\ln(2)x^{2})-18\ln(2)\left(\cos(\sin(x))\right)^{2}\sin(2\ln(2)x^{2})\right)\left(e^{x}\right)^{10}}{2\left(\cos(e)\right)^{9}\left(\sin(\ln(2)x^{2})\right)^{11}}$$