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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

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

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

Beliebte Beispiele

derivative (x-sqrt(x))/(x^{1/5)}

d er i v a t i v e \frac{x - x}{x ^{\frac{1}{5}}}

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

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

derivative of (3x/(4x-2))

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

y^'+(7y)/(x+3)=(x+3)^3

y^{^{'}} + \frac{7 y}{x + 3} = (x + 3)^{3}

integral of t/((t^2+1)^{3/2)}

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