Reelle Funktion/Ableitung/1/Aufgabe/Lösung

Es ist

${}{\begin{aligned}f'(x)&={\frac {{\left(\ln \left(x^{2}+3\right)-x{\sqrt {x^{2}+2}}\right)}'{\left(1+\sin ^{2}x\right)}-{\left(\ln \left(x^{2}+3\right)-x{\sqrt {x^{2}+2}}\right)}{\left(1+\sin ^{2}x\right)}'}{{\left(1+\sin ^{2}x\right)}^{2}}}\\&={\frac {{\left({\frac {2x}{x^{2}+3}}-{\sqrt {x^{2}+2}}-x{\frac {x}{\sqrt {x^{2}+2}}}\right)}{\left(1+\sin ^{2}x\right)}-{\left(\ln \left(x^{2}+3\right)-x{\sqrt {x^{2}+2}}\right)}{\left(2\sin x\cos x\right)}}{{\left(1+\sin ^{2}x\right)}^{2}}}\\&={\frac {{\left({\frac {2x}{x^{2}+3}}-{\frac {2x^{2}+2}{\sqrt {x^{2}+2}}}\right)}{\left(1+\sin ^{2}x\right)}-{\left(\ln \left(x^{2}+3\right)-x{\sqrt {x^{2}+2}}\right)}{\left(2\sin x\cos x\right)}}{{\left(1+\sin ^{2}x\right)}^{2}}}\end{aligned}}$

Zur gelösten Aufgabe