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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

x \to 4 - lim (\frac{1}{x ^{2} - 3 x - 4})

\int \frac{( x - 1 )}{x ^{2}} e^{x} d x

d er i v a t i v e y = (2 x - 9)^{4} (x^{2} + x + 1)^{5}

\frac{d}{d x} (x^{2} (\frac{2}{x ^{2}} + \frac{5}{x ^{3}}))

\frac{d}{d x} (x^{3} + 2 x + 2)