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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

x \to 0 lim (- x^{2} + 1)

\int_{1}^{25} 5 x e^{2 x} d x

\int_{1}^{2} \frac{( x ^{2} - 1 )}{x + 1} d x

d er i v a t i v e f (x) = \frac{c x ^{2}}{x ^{2} + b}

t an g e n t y = ln (7 - 9 x^{2} + 8 x^{4}), at x = 1