(\partial)/(\partial x)(((3x-2y))/(x^2+3y))

Lösung

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

\frac{- 3 x ^{2} + 4 x y + 9 y}{( x ^{2} + 3 y ) ^{2}}

Schritte zur Lösung

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

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

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

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

Multipliziere aus

3 (x^{2} + 3 y) - 2 x (3 x - 2 y) : - 3 x^{2} + 4 x y + 9 y

= \frac{- 3 x ^{2} + 4 x y + 9 y}{( x ^{2} + 3 y ) ^{2}}

\int tan^{6} (a x) d x

\frac{d}{d x} (\frac{2 x + 1}{3 x - 4})

\frac{d}{d x} (2 - 10 x)

\int cos (m x) d x

n \to \infty lim (2 n + 1)