Ratkaise x(x^2+1)^4(23x^3+3x+20)/2sqrt{x^3+1}

$$\frac { x ( x ^ { 2 } + 1 ) ^ { 4 } ( 23 x ^ { 3 } + 3 x + 20 ) } { 2 \sqrt { x ^ { 3 } + 1 } }$$

Laske

$$\frac{x\left(23x^{3}+3x+20\right)\left(x^{2}+1\right)^{4}}{2\sqrt{x^{3}+1}}$$

Derivoi muuttujan x suhteen

$$\frac{\left(x^{2}+1\right)^{3}\left(552\left(x^{3}+1\right)^{\frac{3}{2}}x^{5}-69\sqrt{x^{3}+1}x^{8}+244x^{3}\left(x^{3}+1\right)^{\frac{3}{2}}-78\sqrt{x^{3}+1}x^{6}+360x^{2}\left(x^{3}+1\right)^{\frac{3}{2}}-60\sqrt{x^{3}+1}x^{5}-9\sqrt{x^{3}+1}x^{4}+12x\left(x^{3}+1\right)^{\frac{3}{2}}-60\sqrt{x^{3}+1}x^{3}+40\left(x^{3}+1\right)^{\frac{3}{2}}\right)}{4\left(x^{3}+1\right)^{2}}$$