d/(dy)((4x-2y)/(4x+2y))

Lösung

\frac{d}{d y} (\frac{4 x - 2 y}{4 x + 2 y})

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

Schritte zur Lösung

\frac{d}{d y} (\frac{4 x - 2 y}{4 x + 2 y})

Behandle

x

als Konstante

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d y} (4 x - 2 y) = - 2

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

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

Vereinfache

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

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

\frac{d}{d x} (r (x) (x)^{2} - x^{2})

\frac{d}{d x} ((1 + e^{x})^{3})

l a pl a ce t r an s f or m e^{- 2 t} cos (3 t)

\frac{\partial}{\partial x} (x e^{y} + x^{4} y + y^{3})

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