derivative of (x^2+3x/(-6))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

= \frac{d}{d x} (- \frac{x ^{2} + 3 x}{6})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (3 x) = 3

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

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