derivative f(x)=sqrt(x^2+2x+3)

Lösung

ableitung von

f (x) = x^{2} + 2 x + 3

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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