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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{- x}{x ^{2} + a ^{2}} : - \frac{x}{x ^{2} + a ^{2}}

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

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

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

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

a re a y = 2 x, y = 2 x - 12, y = 0

\frac{\partial}{\partial x} (2 x z)

\int \frac{1}{- t ^{2} + 8 t - 7} d t

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