แก้โจทย์ d/dxln[cos(5x^2)+6x^3]

$$\frac { d } { d x } \ln [ \cos ( 5 x ^ { 2 } ) + 6 x ^ { 3 } ]$$

หาค่า

$$\frac{2x\left(50\left(\cos(x^{2})\right)^{2}\left(\sin(x^{2})\right)^{3}-25\sin(x^{2})\left(\cos(x^{2})\right)^{4}-5\left(\sin(x^{2})\right)^{5}+9x\right)}{-10\left(\sin(x^{2})\right)^{2}\left(\cos(x^{2})\right)^{3}+5\cos(x^{2})\left(\sin(x^{2})\right)^{4}+\left(\cos(x^{2})\right)^{5}+6x^{3}}$$

หาอนุพันธ์ของ w.r.t. x

$$\frac{-4000\left(x\sin(x^{2})\right)^{2}\left(\cos(x^{2})\right)^{8}-4000\left(x\cos(x^{2})\right)^{2}\left(\sin(x^{2})\right)^{8}-8000x^{2}\left(\sin(x^{2})\right)^{4}\left(\cos(x^{2})\right)^{6}-8000x^{2}\left(\cos(x^{2})\right)^{4}\left(\sin(x^{2})\right)^{6}-800x^{2}\left(\sin(x^{2})\right)^{10}-800x^{2}\left(\cos(x^{2})\right)^{10}+4800\left(\sin(x^{2})\right)^{3}\left(\cos(x^{2})\right)^{7}+4800\left(\cos(x^{2})\right)^{3}\left(\sin(x^{2})\right)^{7}-400\sin(x^{2})\left(\cos(x^{2})\right)^{9}-400\cos(x^{2})\left(\sin(x^{2})\right)^{9}-4800\left(x\cos(x^{2})\right)^{5}-24000\left(\cos(x^{2})\right)^{2}\left(x\sin(x^{2})\right)^{3}+48000x^{5}\left(\sin(x^{2})\right)^{2}\left(\cos(x^{2})\right)^{3}-24000x^{5}\cos(x^{2})\left(\sin(x^{2})\right)^{4}+12000x^{3}\sin(x^{2})\left(\cos(x^{2})\right)^{4}+2400x^{3}\left(\sin(x^{2})\right)^{5}-2880x\left(\sin(x^{2})\right)^{2}\left(\cos(x^{2})\right)^{3}+1440x\cos(x^{2})\left(\sin(x^{2})\right)^{4}+288x\left(\cos(x^{2})\right)^{5}-315\left(\sin(2x^{2})\right)^{5}-864x^{4}}{8\left(-10\left(\sin(x^{2})\right)^{2}\left(\cos(x^{2})\right)^{3}+5\cos(x^{2})\left(\sin(x^{2})\right)^{4}+\left(\cos(x^{2})\right)^{5}+6x^{3}\right)^{2}}$$