derivative f(x)=sqrt(x^2+6x-1)

Lösung

ableitung von

f (x) = x^{2} + 6 x - 1

\frac{x + 3}{x ^{2} + 6 x - 1}

Schritte zur Lösung

\frac{d}{d x} (x^{2} + 6 x - 1)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 6 x - 1} \frac{d}{d x} (x^{2} + 6 x - 1)

= \frac{1}{2 x ^{2} + 6 x - 1} \frac{d}{d x} (x^{2} + 6 x - 1)

\frac{d}{d x} (x^{2} + 6 x - 1) = 2 x + 6

= \frac{1}{2 x ^{2} + 6 x - 1} (2 x + 6)

Vereinfache

\frac{1}{2 x ^{2} + 6 x - 1} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x - 1}

= \frac{x + 3}{x ^{2} + 6 x - 1}

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