derivative of sqrt(1+x^2)+x^2sqrt(1+x^2)

Lösung

\frac{d}{d x} (1 + x^{2} + x^{2} 1 + x^{2})

3 x x^{2} + 1

Schritte zur Lösung

\frac{d}{d x} (1 + x^{2} + x^{2} 1 + x^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1 + x^{2}) + \frac{d}{d x} (x^{2} 1 + x^{2})

\frac{d}{d x} (1 + x^{2}) = \frac{x}{1 + x ^{2}}

\frac{d}{d x} (x^{2} 1 + x^{2}) = \frac{3 x ^{3} + 2 x}{1 + x ^{2}}

= \frac{x}{1 + x ^{2}} + \frac{3 x ^{3} + 2 x}{1 + x ^{2}}

Vereinfache

\frac{x}{1 + x ^{2}} + \frac{3 x ^{3} + 2 x}{1 + x ^{2}} : 3 x x^{2} + 1

= 3 x x^{2} + 1

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