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Beliebt Rechnen >

derivative f(x)=1-1/(x^{2/3)}

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - (- \frac{2}{3 x ^{\frac{5}{3}}})

Vereinfache

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

Graph

Beliebte Beispiele

derivative of cos(x)

\frac{d}{d x} (cos (x))

integral of (9x^2-8x+4)

\int (9 x^{2} - 8 x + 4) d x

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n = 1 \sum \infty 8 (\frac{1}{5})^{n}

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x \to 0 + lim (\frac{5 x}{sin ( x )})