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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

derivative of (sinh(x)^{2x^2+2x})

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

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

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

y^'=6y^2+xy^2,y(0)=1

y^{^{'}} = 6 y^{2} + x y^{2}, y (0) = 1

(d^2)/(dx^2)((2000t)/(4t+75))

\frac{d ^{2}}{d x ^{2}} (\frac{2000 t}{4 t + 75})

im pl i c i t x y = 2