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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

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