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

解答

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

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

求解步骤

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

将

y

视为常数

使用微分除法定则:

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

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

\frac{\partial}{\partial x} (x - 3 y) = 1

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

= \frac{1 \cdot ( 2 x y + 3 ) - 2 y ( x - 3 y )}{( 2 x y + 3 ) ^{2}}

化简

\frac{1 \cdot ( 2 x y + 3 ) - 2 y ( x - 3 y )}{( 2 x y + 3 ) ^{2}} : \frac{6 y ^{2} + 3}{( 2 x y + 3 ) ^{2}}

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

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

\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

\int 3 cos (10 x) d x

\frac{d}{d x} (lo g_{5} (x^{4} 2 x^{2} + 9 x))

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