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Beliebt Rechnen >

derivative 9/((9-x^6)^{3/2)}

Lösung

ableitung von

\frac{9}{( 9 - x ^{6} ) ^{\frac{3}{2}}}

Lösung

\frac{81 x ^{5}}{( 9 - x ^{6} ) ^{\frac{5}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9}{( 9 - x ^{6} ) ^{\frac{3}{2}}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (\frac{1}{( 9 - x ^{6} ) ^{\frac{3}{2}}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 9 \frac{d}{d x} ((9 - x^{6})^{- \frac{3}{2}})

Wende die Kettenregel an:

- \frac{3}{2 ( 9 - x ^{6} ) ^{\frac{5}{2}}} \frac{d}{d x} (9 - x^{6})

= - \frac{3}{2 ( 9 - x ^{6} ) ^{\frac{5}{2}}} \frac{d}{d x} (9 - x^{6})

\frac{d}{d x} (9 - x^{6}) = - 6 x^{5}

= 9 (- \frac{3}{2 ( 9 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5}))

Vereinfache

9 (- \frac{3}{2 ( 9 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5})) : \frac{81 x ^{5}}{( 9 - x ^{6} ) ^{\frac{5}{2}}}

= \frac{81 x ^{5}}{( 9 - x ^{6} ) ^{\frac{5}{2}}}

Graph

Beliebte Beispiele

integral of xsqrt(9-x^2)

\int x 9 - x^{2} d x

limit as x approaches 0 of (x^2-1)/x

x \to 0 lim (\frac{x ^{2} - 1}{x})

laplacetransform (t^2*e^{-,\at})

l a pl a ce t r an s f or m (t^{2} \cdot e^{-, at})

derivative of xsqrt(x-x^2)

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

(dy)/(dx)=(6y)/(5x)

\frac{d y}{d x} = \frac{6 y}{5 x}