(\partial)/(\partial x)(((2x-y))/(5x+3y))

Lösung

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{5 x + 3 y})

\frac{11 y}{( 5 x + 3 y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{5 x + 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} ( 2 x - y ) ( 5 x + 3 y ) - \frac{\partial}{\partial x} ( 5 x + 3 y ) ( 2 x - y )}{( 5 x + 3 y ) ^{2}}

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

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= \frac{2 ( 5 x + 3 y ) - 5 ( 2 x - y )}{( 5 x + 3 y ) ^{2}}

Multipliziere aus

2 (5 x + 3 y) - 5 (2 x - y) : 11 y

= \frac{11 y}{( 5 x + 3 y ) ^{2}}

x^{2} y^{^{''}} + x y^{^{'}} - y = ln (x)

\int \frac{x}{1 - 2 x ^{2}} d x

\int_{2}^{4} x^{2} d x

\int_{1}^{4} (3 x^{3} + x + 1) d x

\frac{d}{d x} (\frac{3}{8 x ^{\frac{5}{2}}})