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

Lösung

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

\frac{4 x y}{( x ^{2} + y ) ^{2}}

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

2 x (x^{2} + y) - 2 x (x^{2} - y) : 4 x y

= \frac{4 x y}{( x ^{2} + y ) ^{2}}

\int \frac{8 cosh ( x )}{x} d x

\int \frac{( 5 - x )}{2 x ^{2} + x - 1} d x

z \to 2 lim (\frac{z ^{2} + 3}{i z})

t a y l or ln (1 + 7 x)

\frac{d ^{2}}{d x ^{2}} (4 x + 15)