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Beliebt Rechnen >

(\partial)/(\partial x)(x/(x+y))

Lösung

\frac{\partial}{\partial x} (\frac{x}{x + y})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x + y})

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

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

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

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

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

1 \cdot (x + y) - 1 \cdot x = y

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

Beliebte Beispiele

(\partial)/(\partial y)(ln(x-5y))

\frac{\partial}{\partial y} (ln (x - 5 y))

fläche x^2+4x+3,y=-2,-2<x<0

a re a x^{2} + 4 x + 3, y = - 2, - 2 < x < 0

fläche x=y+2,x=y^2

a re a x = y + 2, x = y^{2}

derivative 1/(7-6e^x)

d er i v a t i v e \frac{1}{7 - 6 e ^{x}}

(\partial)/(\partial x)(-400x(y-x^2)-2(1-x))

\frac{\partial}{\partial x} (- 400 x (y - x^{2}) - 2 (1 - x))