(\partial)/(\partial x)(a/(x^2+a^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial 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}}

d er i v a t i v e ln (8 x + 9)

\int (a^{\frac{2}{3}} - x^{\frac{2}{3}}) d x

\int \frac{1}{36 - 4 x ^{2}} d x

\int (4 - 2 x) d x

\frac{d}{d x} (sin (x) + x)