derivative f(x)=sqrt(x^2+12)

Lösung

ableitung von

f (x) = x^{2} + 12

\frac{x}{x ^{2} + 12}

Schritte zur Lösung

\frac{d}{d x} (x^{2} + 12)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 12} \frac{d}{d x} (x^{2} + 12)

= \frac{1}{2 x ^{2} + 12} \frac{d}{d x} (x^{2} + 12)

\frac{d}{d x} (x^{2} + 12) = 2 x

= \frac{1}{2 x ^{2} + 12} \cdot 2 x

Vereinfache

\frac{1}{2 x ^{2} + 12} \cdot 2 x : \frac{x}{x ^{2} + 12}

= \frac{x}{x ^{2} + 12}

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