(\partial)/(\partial x)((5x-6y)/(5x+6y))

Lösung

\frac{\partial}{\partial x} (\frac{5 x - 6 y}{5 x + 6 y})

\frac{60 y}{( 5 x + 6 y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{5 x - 6 y}{5 x + 6 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} ( 5 x - 6 y ) ( 5 x + 6 y ) - \frac{\partial}{\partial x} ( 5 x + 6 y ) ( 5 x - 6 y )}{( 5 x + 6 y ) ^{2}}

\frac{\partial}{\partial x} (5 x - 6 y) = 5

\frac{\partial}{\partial x} (5 x + 6 y) = 5

= \frac{5 ( 5 x + 6 y ) - 5 ( 5 x - 6 y )}{( 5 x + 6 y ) ^{2}}

Multipliziere aus

5 (5 x + 6 y) - 5 (5 x - 6 y) : 60 y

= \frac{60 y}{( 5 x + 6 y ) ^{2}}

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