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

Lösung

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

\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}}

\int_{0}^{\infty} \frac{x}{x ^{3} + 1} d x

x \to 3 lim (\frac{4 x - 5}{5 x - 1})

\int + x^{2} x^{3} + 27 d x

\frac{d y}{d x} = e^{3 x - 2 y}

n = 1 \sum \infty (\frac{10}{11})^{n}