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Beliebt Rechnen >

derivative f(x)=x^4+4x^3-48x^2+6

Lösung

ableitung von

f (x) = x^{4} + 4 x^{3} - 48 x^{2} + 6

Lösung

4 x^{3} + 12 x^{2} - 96 x

Schritte zur Lösung

\frac{d}{d x} (x^{4} + 4 x^{3} - 48 x^{2} + 6)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{4}) + \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (48 x^{2}) + \frac{d}{d x} (6)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (48 x^{2}) = 96 x

\frac{d}{d x} (6) = 0

= 4 x^{3} + 12 x^{2} - 96 x + 0

Vereinfache

= 4 x^{3} + 12 x^{2} - 96 x

Graph

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