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Beliebt Rechnen >

derivative of 1/(6+x^2)

Lösung

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

Lösung

- \frac{2 x}{( 6 + x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{( 6 + x ^{2} ) ^{2}} \frac{d}{d x} (6 + x^{2})

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

\frac{d}{d x} (6 + x^{2}) = 2 x

= - \frac{1}{( 6 + x ^{2} ) ^{2}} \cdot 2 x

Vereinfache

- \frac{1}{( 6 + x ^{2} ) ^{2}} \cdot 2 x : - \frac{2 x}{( 6 + x ^{2} ) ^{2}}

= - \frac{2 x}{( 6 + x ^{2} ) ^{2}}

Graph

Beliebte Beispiele

derivative y=(e^x)/x

d er i v a t i v e y = \frac{e ^{x}}{x}

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\int \frac{1}{sin ^{2} ( x ) \cdot cos ^{2} ( x )} d x

y^{''}+6y^'+9y=(e^{-3x})/x

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3 x}}{x}