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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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