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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as x approaches-infinity of x^n

derivative F(x)=(x^3-3x^2+4x-5)/(x^2)

f(x)=e^{-x^2}+x

y^'+4y=x^2e^{-4x}