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Beliebt Rechnen >

(\partial)/(\partial y)((-y)/(x^2+9y^2))

Lösung

\frac{\partial}{\partial y} (\frac{- y}{x ^{2} + 9 y ^{2}})

Lösung

- \frac{x ^{2} - 9 y ^{2}}{( x ^{2} + 9 y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{- y}{x ^{2} + 9 y ^{2}})

Vereinfache

\frac{- y}{x ^{2} + 9 y ^{2}} : - \frac{y}{x ^{2} + 9 y ^{2}}

= \frac{\partial}{\partial y} (- \frac{y}{x ^{2} + 9 y ^{2}})

Behandle

x

als Konstante

Entferne die Konstante:

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

= - \frac{\partial}{\partial y} (\frac{y}{x ^{2} + 9 y ^{2}})

Wende die Quotientenregel an:

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

= - \frac{\frac{\partial}{\partial y} ( y ) ( x ^{2} + 9 y ^{2} ) - \frac{\partial}{\partial y} ( x ^{2} + 9 y ^{2} ) y}{( x ^{2} + 9 y ^{2} ) ^{2}}

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (x^{2} + 9 y^{2}) = 18 y

= - \frac{1 \cdot ( x ^{2} + 9 y ^{2} ) - 18 yy}{( x ^{2} + 9 y ^{2} ) ^{2}}

1 \cdot (x^{2} + 9 y^{2}) - 18 yy = x^{2} - 9 y^{2}

= - \frac{x ^{2} - 9 y ^{2}}{( x ^{2} + 9 y ^{2} ) ^{2}}

Beliebte Beispiele

integral from-2 to 3 of (40)/(x^4)

\int_{- 2}^{3} \frac{40}{x ^{4}} d x

derivative y=sqrt(x+3)

d er i v a t i v e y = x + 3

inverselaplace 1/s-2/((s+3)^2-9)

in v erse l a pl a ce \frac{1}{s} - \frac{2}{( s + 3 ) ^{2} - 9}

integral of (2x^2-1)/(x^3-x)

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

integral of 1/(x^4+y^2)

\int \frac{1}{x ^{4} + y ^{2}} d y