แก้โจทย์ d/dx[cos^4(2x)+tan^3(logx)]

$$\frac { d } { d x } [ \cos ^ { 4 } ( 2 x ) + \tan ^ { 3 } ( \log x ) ]$$

หาค่า

$$4\left(\sin(x)+\cos(x)\right)^{3}\left(\cos(x)-\sin(x)\right)^{5}-4\left(\cos(x)-\sin(x)\right)^{3}\left(\sin(x)+\cos(x)\right)^{5}+\frac{3\log(e)\left(\tan(\log(x))\right)^{2}}{x\left(\cos(\log(x))\right)^{2}}$$

หาอนุพันธ์ของ w.r.t. x

$$\frac{-288\left(\ln(10)x\sin(x)\right)^{2}\left(\cos(\log(x))\right)^{5}\left(\cos(x)\right)^{6}-288\left(\ln(10)x\cos(x)\right)^{2}\left(\cos(\log(x))\right)^{5}\left(\sin(x)\right)^{6}-100\left(\ln(10)x\right)^{2}\left(\sin(2x)\right)^{4}\left(\cos(\log(x))\right)^{5}+152\left(\ln(10)x\sin(2x)\right)^{2}\left(\cos(\log(x))\right)^{5}-16\left(\ln(10)x\right)^{2}\left(\cos(\log(x))\right)^{5}-3\ln(10)\cos(\log(x))\left(\sin(\log(x))\right)^{2}+6\sin(\log(x))\left(\cos(\log(x))\right)^{2}+12\left(\sin(\log(x))\right)^{3}}{\left(\ln(10)x\right)^{2}\left(\cos(\log(x))\right)^{5}}$$