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Beliebt Rechnen >

(\partial}{\partial x}(\frac{x-y)/x)

Lösung

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

Lösung

\frac{y}{x ^{2}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

= \frac{y}{x ^{2}}

Beliebte Beispiele

derivative of ln(x/4 (x-4))

\frac{d}{d x} (ln (\frac{x}{4}) (x - 4))

integral of (sin(x))/(cot(x))

\int \frac{sin ( x )}{cot ( x )} d x

inverselaplace s/(s^2-16)

in v erse l a pl a ce \frac{s}{s ^{2} - 16}

y^'=x^2-y-2,y(0)=1

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

integral of (x^2)/((x^2-2x+2)^2)

\int \frac{x ^{2}}{( x ^{2} - 2 x + 2 ) ^{2}} d x