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

Lösung

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

\frac{6 y}{( 3 x + y ) ^{2}}

Schritte zur Lösung

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

\frac{\partial}{\partial x} (3 x - y) = 3

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

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

Multipliziere aus

3 (3 x + y) - 3 (3 x - y) : 6 y

= \frac{6 y}{( 3 x + y ) ^{2}}

\int x (2 x - 1)^{9} d x

\frac{d}{d x} (8 x - 8 e^{x})

t an g e n t f (x) = x^{2} - 9, (4, 7)

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

6 x + 10, 4 x + 44, x = 15, x = 19