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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

limit as x approaches infinity of 2^x+1

x \to \infty lim (2^{x} + 1)

limit as x approaches-2 of f(x)

x \to - 2 lim (f (x))

integral from-3 to 3 of x^2-9

\int_{- 3}^{3} x^{2} - 9 d x

(xsec(y/x)+y)dx-xdy=0

(x sec (\frac{y}{x}) + y) d x - x d y = 0

y=(2^x)/2+(12)/(sqrt(x))

y = \frac{2 ^{x}}{2} + \frac{12}{x}