(\partial)/(\partial x)(((ax+by))/(cx+dy))

Lösung

\frac{\partial}{\partial x} (\frac{( a x + b y )}{c x + d y})

\frac{- b yc + a y d}{( x c + y d ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{( a x + b y )}{c x + d y})

Behandle

a, b, y, c, d

als Konstanten

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( a x + b y ) ( c x + d y ) - \frac{\partial}{\partial x} ( c x + d y ) ( a x + b y )}{( c x + d y ) ^{2}}

\frac{\partial}{\partial x} (a x + b y) = a

\frac{\partial}{\partial x} (c x + d y) = c

= \frac{a ( c x + d y ) - c ( a x + b y )}{( c x + d y ) ^{2}}

Multipliziere aus

a (c x + d y) - c (a x + b y) : - b yc + a y d

= \frac{- b yc + a y d}{( x c + y d ) ^{2}}

x y^{^{''}} + y^{^{'}} = 1

\frac{\partial}{\partial x} (6 x sin (x + 2 y - z))

\frac{\partial}{\partial y} (2 x^{2} + 2 y - 8)

\int (csc^{2} (x) + 4) d x

\frac{d}{d x} (x^{2} \cdot e^{2 x})