(\partial)/(\partial x)((4x-2y)/(3x^2+2y))

解答

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

\frac{- 12 x ^{2} + 12 x y + 8 y}{( 3 x ^{2} + 2 y ) ^{2}}

求解步骤

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

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

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

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

= \frac{4 ( 3 x ^{2} + 2 y ) - 6 x ( 4 x - 2 y )}{( 3 x ^{2} + 2 y ) ^{2}}

乘开

4 (3 x^{2} + 2 y) - 6 x (4 x - 2 y) : - 12 x^{2} + 12 x y + 8 y

= \frac{- 12 x ^{2} + 12 x y + 8 y}{( 3 x ^{2} + 2 y ) ^{2}}

\frac{d y}{d x} = \frac{- 2 x y + 1}{x ^{2} + 2 y}

t an g e n t - \frac{7}{2} x^{2} + 5 x + 5

\int x^{b - 1} e^{x^{b}} d x

\int 200 - 4 t d t

\frac{d}{d x} (lo g_{10} (\frac{2 x}{1 + x ^{2}}))