derivative f(x)=x^{5/3}-x^{2/3}

Lösung

ableitung von

f (x) = x^{\frac{5}{3}} - x^{\frac{2}{3}}

\frac{5 x - 2}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{5}{3}} - x^{\frac{2}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{\frac{5}{3}}) - \frac{d}{d x} (x^{\frac{2}{3}})

\frac{d}{d x} (x^{\frac{5}{3}}) = \frac{5 x ^{\frac{2}{3}}}{3}

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

= \frac{5 x ^{\frac{2}{3}}}{3} - \frac{2}{3 x ^{\frac{1}{3}}}

Vereinfache

\frac{5 x ^{\frac{2}{3}}}{3} - \frac{2}{3 x ^{\frac{1}{3}}} : \frac{5 x - 2}{3 x ^{\frac{1}{3}}}

= \frac{5 x - 2}{3 x ^{\frac{1}{3}}}

l a pl a ce t r an s f or m e^{- t} t

ma c l a u r in \frac{1}{x - 3}

\int \frac{2 e ^{2 r}}{7 + e ^{2 r}} d r

\frac{d}{d x} (5^{6^{7^{x}}})

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