Ratkaise [ln(1+x^2)+2/x^2-1-sqrt{1+x^2}]^prime

$$[ \ln ( 1 + x ^ { 2 } ) + \frac { 2 } { x ^ { 2 } - 1 } - \sqrt { 1 + x ^ { 2 } } ] ^ { \prime }$$

Laske

$$\frac{x\left(-x^{6}+2\sqrt{x^{2}+1}x^{4}+x^{4}-8\sqrt{x^{2}+1}x^{2}+x^{2}-2\sqrt{x^{2}+1}-1\right)}{\left(x^{2}+1\right)^{\frac{3}{2}}\left(x^{2}-1\right)^{2}}$$

Derivoi muuttujan x suhteen

$$\frac{10\left(x^{2}+1\right)^{\frac{3}{2}}x^{6}-12\sqrt{x^{2}+1}x^{8}-x^{8}+44\sqrt{x^{2}+1}x^{6}-34\left(x^{2}+1\right)^{\frac{3}{2}}x^{4}+2x^{6}+22x^{2}\left(x^{2}+1\right)^{\frac{3}{2}}+28\sqrt{x^{2}+1}x^{4}+4\sqrt{x^{2}+1}x^{2}+2\left(x^{2}+1\right)^{\frac{3}{2}}-2x^{2}+1}{\left(x^{2}+1\right)^{\frac{5}{2}}\left(x^{2}-1\right)^{3}}$$