derivative of a/(x^2+a^2)

Lösung

\frac{d}{d x} (\frac{a}{x ^{2} + a ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{a}{x ^{2} + a ^{2}})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t)

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