derivative of 3/4 x^{4/3}-3/8 x^{2/3}+8

Lösung

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

\frac{- 1 + 4 x ^{\frac{2}{3}}}{4 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Vereinfache

\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 8 : \frac{3 x ^{\frac{4}{3}}}{4} - \frac{3 x ^{\frac{2}{3}}}{8} + 8

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{3 x ^{\frac{4}{3}}}{4}) = x^{\frac{1}{3}}

\frac{d}{d x} (\frac{3 x ^{\frac{2}{3}}}{8}) = \frac{1}{4 x ^{\frac{1}{3}}}

\frac{d}{d x} (8) = 0

= x^{\frac{1}{3}} - \frac{1}{4 x ^{\frac{1}{3}}} + 0

Vereinfache

x^{\frac{1}{3}} - \frac{1}{4 x ^{\frac{1}{3}}} + 0 : \frac{- 1 + 4 x ^{\frac{2}{3}}}{4 x ^{\frac{1}{3}}}

= \frac{- 1 + 4 x ^{\frac{2}{3}}}{4 x ^{\frac{1}{3}}}

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