derivative of 2/(1+4x^2)

Lösung

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

- \frac{16 x}{( 1 + 4 x ^{2} ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 (- \frac{1}{( 1 + 4 x ^{2} ) ^{2}} \cdot 8 x) : - \frac{16 x}{( 1 + 4 x ^{2} ) ^{2}}

= - \frac{16 x}{( 1 + 4 x ^{2} ) ^{2}}

\int \frac{x ^{2}}{36 + x ^{2}} d x

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