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Beliebt Rechnen >

derivative of w/(sqrt(1-4x^2))

Lösung

\frac{d}{d x} (\frac{w}{1 - 4 x ^{2}})

Lösung

\frac{4 w x}{( 1 - 4 x ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{w}{1 - 4 x ^{2}})

Behandle

w

als Konstante

Entferne die Konstante:

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

= w \frac{d}{d x} (\frac{1}{1 - 4 x ^{2}})

Wende Exponentenregel an:

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

= w \frac{d}{d x} ((1 - 4 x^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 1 - 4 x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 - 4 x^{2})

= - \frac{1}{2 ( 1 - 4 x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 - 4 x^{2})

\frac{d}{d x} (1 - 4 x^{2}) = - 8 x

= w (- \frac{1}{2 ( 1 - 4 x ^{2} ) ^{\frac{3}{2}}} (- 8 x))

Vereinfache

w (- \frac{1}{2 ( 1 - 4 x ^{2} ) ^{\frac{3}{2}}} (- 8 x)) : \frac{4 w x}{( 1 - 4 x ^{2} ) ^{\frac{3}{2}}}

= \frac{4 w x}{( 1 - 4 x ^{2} ) ^{\frac{3}{2}}}

Graph

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