ແກ້ d^2/dx^2(arcsin^3ln(x^2+1))

$$\frac { d ^ { 2 } } { d x ^ { 2 } } ( \arcsin ^ { 3 } \ln ( x ^ { 2 } + 1 ) )$$

ປະເມີນ

$$\frac{6\arcsin(\ln(x^{2}+1))\left(\arcsin(\ln(x^{2}+1))\left(x\ln(x^{2}+1)\right)^{2}-\arcsin(\ln(x^{2}+1))\ln(x^{2}+1)^{2}+2x^{2}\ln(x^{2}+1)\arcsin(\ln(x^{2}+1))-x^{2}\arcsin(\ln(x^{2}+1))+4x^{2}\sqrt{-\ln(x^{2}+1)^{2}+1}+\arcsin(\ln(x^{2}+1))\right)}{\left(x^{2}+1\right)^{2}\left(-\ln(x^{2}+1)^{2}+1\right)^{\frac{3}{2}}}$$

ບອກຄວາມແຕກຕ່າງ w.r.t. x

$$\frac{12x\left(\ln(x^{2}+1)^{4}\left(x\arcsin(\ln(x^{2}+1))\right)^{2}+3\ln(x^{2}+1)^{3}\left(x\arcsin(\ln(x^{2}+1))\right)^{2}+6\left(\ln(x^{2}+1)\arcsin(\ln(x^{2}+1))\right)^{2}+2\left(x\ln(x^{2}+1)\arcsin(\ln(x^{2}+1))\right)^{2}-3\left(\arcsin(\ln(x^{2}+1))\right)^{2}\ln(x^{2}+1)^{4}-6x^{2}\arcsin(\ln(x^{2}+1))\left(-\ln(x^{2}+1)^{2}+1\right)^{\frac{3}{2}}-3\ln(x^{2}+1)\left(x\arcsin(\ln(x^{2}+1))\right)^{2}-3\left(\arcsin(\ln(x^{2}+1))\right)^{2}\ln(x^{2}+1)^{3}+12x^{2}\ln(x^{2}+1)\arcsin(\ln(x^{2}+1))\sqrt{-\ln(x^{2}+1)^{2}+1}+6\arcsin(\ln(x^{2}+1))\left(-\ln(x^{2}+1)^{2}+1\right)^{\frac{3}{2}}+3\left(x\arcsin(\ln(x^{2}+1))\right)^{2}-4\left(x\ln(x^{2}+1)\right)^{2}+3\ln(x^{2}+1)\left(\arcsin(\ln(x^{2}+1))\right)^{2}-3\left(\arcsin(\ln(x^{2}+1))\right)^{2}+4x^{2}\right)}{\left(x^{2}+1\right)^{3}\left(-\ln(x^{2}+1)^{2}+1\right)^{\frac{5}{2}}}$$