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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

Multipliziere aus

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

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

\frac{d}{d x} (e^{a x} sin (b x))

x^{2} \frac{d y}{d x} = 1 - x^{2} + y^{2} - x^{2} y^{2}

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

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

d er i v a t i v e \frac{x - 13}{x - 13}