derivative of-1/6 x^3-1/2 x^2+x+1+ke^k

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (1) = 0

\frac{d}{d x} (k e^{k}) = 0

= - \frac{x ^{2}}{2} - x + 1 + 0 + 0

Vereinfache

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

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