derivative y=x^{4/5}(x-3)

Lösung

ableitung von

y = x^{\frac{4}{5}} (x - 3)

\frac{9 x - 12}{5 x ^{\frac{1}{5}}}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{4}{5}} (x - 3))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{4}{5}}, g = x - 3

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 3) + \frac{d}{d x} (x - 3) x^{\frac{4}{5}}

\frac{d}{d x} (x^{\frac{4}{5}}) = \frac{4}{5 x ^{\frac{1}{5}}}

\frac{d}{d x} (x - 3) = 1

= \frac{4}{5 x ^{\frac{1}{5}}} (x - 3) + 1 \cdot x^{\frac{4}{5}}

Vereinfache

\frac{4}{5 x ^{\frac{1}{5}}} (x - 3) + 1 \cdot x^{\frac{4}{5}} : \frac{9 x - 12}{5 x ^{\frac{1}{5}}}

= \frac{9 x - 12}{5 x ^{\frac{1}{5}}}

\frac{d}{d x} (\frac{- 2 x ^{2} + 25}{25 - x ^{2}})

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