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Beliebt Rechnen >

derivative of x^3-5x^2+4x-20-5e^{3x}

Lösung

\frac{d}{d x} (x^{3} - 5 x^{2} + 4 x - 20 - 5 e^{3 x})

Lösung

3 x^{2} - 10 x - 15 e^{3 x} + 4

Schritte zur Lösung

\frac{d}{d x} (x^{3} - 5 x^{2} + 4 x - 20 - 5 e^{3 x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (4 x) - \frac{d}{d x} (20) - \frac{d}{d x} (5 e^{3 x})

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

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d}{d x} (4 x) = 4

\frac{d}{d x} (20) = 0

\frac{d}{d x} (5 e^{3 x}) = 15 e^{3 x}

= 3 x^{2} - 10 x + 4 - 0 - 15 e^{3 x}

Vereinfache

= 3 x^{2} - 10 x - 15 e^{3 x} + 4

Graph

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