(\partial)/(\partial y)(y/(2x+3y))

Lösung

\frac{\partial}{\partial y} (\frac{y}{2 x + 3 y})

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

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{y}{2 x + 3 y})

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 ) ( 2 x + 3 y ) - \frac{\partial}{\partial y} ( 2 x + 3 y ) y}{( 2 x + 3 y ) ^{2}}

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

\frac{\partial}{\partial y} (2 x + 3 y) = 3

= \frac{1 \cdot ( 2 x + 3 y ) - 3 y}{( 2 x + 3 y ) ^{2}}

Vereinfache

= \frac{2 x}{( 2 x + 3 y ) ^{2}}

\int_{0}^{2 π} (cos (x))^{2} d x

d er i v a t i v e \frac{2 x ^{2} + 6 x + 2}{x}

\int sec^{2} (x) tan (x) d x

n = 1 \sum \infty (sin (3))^{n}

\frac{d}{d x} (e^{x + y} - 1)