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Beliebt Rechnen >

derivative f(x)=2x^4+x^3-x^2+4

Lösung

ableitung von

f (x) = 2 x^{4} + x^{3} - x^{2} + 4

Lösung

8 x^{3} + 3 x^{2} - 2 x

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (2 x^{4}) = 8 x^{3}

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

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

\frac{d}{d x} (4) = 0

= 8 x^{3} + 3 x^{2} - 2 x + 0

Vereinfache

= 8 x^{3} + 3 x^{2} - 2 x

Graph

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