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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

c, y

als Konstante

Entferne die Konstante:

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

= - c \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}}

= - c \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

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

Vereinfache

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

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

Beliebte Beispiele

integral from 1 to 3 of 1/(4+(x-1)^2)

\int_{1}^{3} \frac{1}{4 + ( x - 1 ) ^{2}} d x

integral of 24xy^2+3ye^{xy}

\int 24 x y^{2} + 3 y e^{x y} d x

(dy)/(dx)=e^{(6x-3y)},y(0)=3

\frac{d y}{d x} = e^{(6 x - 3 y)}, y (0) = 3

integral of (2-e^x)^2

\int (2 - e^{x})^{2} d x

derivative f(x)=x^2(1-5x)

d er i v a t i v e f (x) = x^{2} (1 - 5 x)