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Beliebt Rechnen >

derivative x^{1/3}-x^{-2/3}

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

limit as x approaches+0 of 2x^2cos(5/x)

x \to + 0 lim (2 x^{2} cos (\frac{5}{x}))

(\partial)/(\partial x)(e^x-2-cos(xy))

\frac{\partial}{\partial x} (e^{x} - 2 - cos (x y))

derivative of 3/(5+x)

\frac{d}{d x} (\frac{3}{5 + x})

integral of 1/(sqrt(x)+4)

\int \frac{1}{x + 4} d x

y^'=(2cos(y))/(sin(y))

y^{^{'}} = \frac{2 cos ( y )}{sin ( y )}