derivative of x^4-12x^3+48x^2-64x

Lösung

\frac{d}{d x} (x^{4} - 12 x^{3} + 48 x^{2} - 64 x)

4 x^{3} - 36 x^{2} + 96 x - 64

Schritte zur Lösung

\frac{d}{d x} (x^{4} - 12 x^{3} + 48 x^{2} - 64 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (12 x^{3}) + \frac{d}{d x} (48 x^{2}) - \frac{d}{d x} (64 x)

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

\frac{d}{d x} (12 x^{3}) = 36 x^{2}

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

\frac{d}{d x} (64 x) = 64

= 4 x^{3} - 36 x^{2} + 96 x - 64

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