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Beliebt Rechnen >

derivative p(x)=x^4-3x^3+10x^2-6x-20

Lösung

ableitung von

p (x) = x^{4} - 3 x^{3} + 10 x^{2} - 6 x - 20

Lösung

4 x^{3} - 9 x^{2} + 20 x - 6

Schritte zur Lösung

\frac{d}{d x} (x^{4} - 3 x^{3} + 10 x^{2} - 6 x - 20)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (10 x^{2}) - \frac{d}{d x} (6 x) - \frac{d}{d x} (20)

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

\frac{d}{d x} (10 x^{2}) = 20 x

\frac{d}{d x} (6 x) = 6

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

= 4 x^{3} - 9 x^{2} + 20 x - 6 - 0

Vereinfache

= 4 x^{3} - 9 x^{2} + 20 x - 6

Graph

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