(\partial)/(\partial y)(y/(y-2x))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d v}{d t} = 9.8 - \frac{v}{5}, v (0) = 0

x y^{^{'}} = x + y

\frac{d}{d x} (\frac{K x + 11}{x ^{2} + ( K + 1 ) x + 11})

\int sin (9 x) cos (5 x) d x

x \to 0 lim (8 x cot (3 x))