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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{4 x y}{( x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

= 2 x \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

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

Vereinfache

2 x (- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 2 y) : - \frac{4 x y}{( x ^{2} + y ^{2} ) ^{2}}

= - \frac{4 x y}{( x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

derivative of (4-x^2^3)

\frac{d}{d x} ((4 - x^{2})^{3})

integral of (sin(2/x))/(x^2)

\int \frac{sin ( \frac{2}{x} )}{x ^{2}} d x

derivative of 5/3 x^2y^{-2}

\frac{d}{d x} (\frac{5}{3} x^{2} y^{- 2})

integral of 2/(sqrt(x^2+9))

\int \frac{2}{x ^{2} + 9} d x

sum from n=0 to infinity of n/(1+n^2)

n = 0 \sum \infty \frac{n}{1 + n ^{2}}