d/(dy)(y/(x^2+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Quotientenregel an:

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

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

\frac{d y}{d y} = 1

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

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

1 \cdot (x^{2} + y^{2}) - 2 yy = x^{2} - y^{2}

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

\int \frac{3 x ^{2}}{( x ^{3} + 1 ) ^{5}} d x

\frac{d}{d x} (\frac{x}{( 2 x - 1 ) ^{6}})

\int (4 x + 3)^{3} d x

f (x) = e^{x^{2}} \cdot 2 x

\int 5 x^{3} 1 - x^{2} d x