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Beliebt Rechnen >

(\partial)/(\partial y)((ax+by)/(cx+dy))

Lösung

\frac{\partial}{\partial y} (\frac{a x + b y}{c x + d y})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{a x + b y}{c x + d y})

Behandle

a, x, b, c, d

als Konstanten

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial y} ( a x + b y ) ( c x + d y ) - \frac{\partial}{\partial y} ( c x + d y ) ( a x + b y )}{( c x + d y ) ^{2}}

\frac{\partial}{\partial y} (a x + b y) = b

\frac{\partial}{\partial y} (c x + d y) = d

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

Multipliziere aus

b (c x + d y) - d (a x + b y) : x b c - a x d

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

Beliebte Beispiele

integral of (cos^3(x))/(1+sin(x))

\int \frac{cos ^{3} ( x )}{1 + sin ( x )} d x

integral of 1/(sqrt(x^2-100))

\int \frac{1}{x ^{2} - 100} d x

integral of x/(sqrt(1-16x^2))

\int \frac{x}{1 - 16 x ^{2}} d x

derivative of 2sin(x-sin(2x))

\frac{d}{d x} (2 sin (x) - sin (2 x))

derivative of (x^2-4x/((x-2)^2))

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