derivative of 4/3 x^3-4x+3

Lösung

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

4 x^{2} - 4

Schritte zur Lösung

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

Vereinfache

\frac{4}{3} x^{3} - 4 x + 3 : \frac{4 x ^{3}}{3} - 4 x + 3

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (3) = 0

= 4 x^{2} - 4 + 0

Vereinfache

= 4 x^{2} - 4

f (x) = \frac{1}{x - 4}

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