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Beliebt Rechnen >

(\partial)/(\partial y)((x^2)/(4-y^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

= x^{2} \frac{\partial}{\partial y} (\frac{1}{4 - y ^{2}})

Wende Exponentenregel an:

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

= x^{2} \frac{\partial}{\partial y} ((4 - y^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 4 - y ^{2} ) ^{2}} \frac{\partial}{\partial y} (4 - y^{2})

= - \frac{1}{( 4 - y ^{2} ) ^{2}} \frac{\partial}{\partial y} (4 - y^{2})

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

= x^{2} (- \frac{1}{( 4 - y ^{2} ) ^{2}} (- 2 y))

Vereinfache

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

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

Beliebte Beispiele

(\partial)/(\partial p)((p+q)/(p+r))

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

derivative 1/(d+ke^d)

d er i v a t i v e \frac{1}{d + k e ^{d}}

(d^2)/(dx^2)y+36y=0

\frac{d ^{2}}{d x ^{2}} y + 36 y = 0

(\partial)/(\partial x)(5e^{xy})

\frac{\partial}{\partial x} (5 e^{x y})

derivative of (3x-5/(x^2+7))

\frac{d}{d x} (\frac{3 x - 5}{x ^{2} + 7})