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Beliebt Rechnen >

(\partial)/(\partial x)((-3x)/(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{- 3 x}{x ^{2} + y ^{2}})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{- 3 x}{x ^{2} + y ^{2}})

Vereinfache

\frac{- 3 x}{x ^{2} + y ^{2}} : - \frac{3 x}{x ^{2} + y ^{2}}

= \frac{\partial}{\partial x} (- \frac{3 x}{x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= - 3 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}})

Wende die Quotientenregel an:

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

= - 3 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + y ^{2} ) - \frac{\partial}{\partial x} ( x ^{2} + y ^{2} ) x}{( x ^{2} + y ^{2} ) ^{2}}

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

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

= - 3 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}}

Vereinfache

- 3 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}} : - \frac{3 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

= - \frac{3 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

integral of 1/(x^2+b)

\int \frac{1}{x ^{2} + b} d x

integral of e^3

\int e^{3} d x

xy^'-y=-x^2+x-1

x y^{^{'}} - y = - x^{2} + x - 1

integral of x^2sqrt(2-x^2)

\int x^{2} 2 - x^{2} d x

(\partial)/(\partial x)(sqrt(8-x^2-3y^2))

\frac{\partial}{\partial x} (8 - x^{2} - 3 y^{2})