(\partial)/(\partial x)((9x-2y)/(9x+2y))

解答

\frac{\partial}{\partial x} (\frac{9 x - 2 y}{9 x + 2 y})

\frac{36 y}{( 9 x + 2 y ) ^{2}}

求解步骤

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

\frac{\partial}{\partial x} (9 x - 2 y) = 9

\frac{\partial}{\partial x} (9 x + 2 y) = 9

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

乘开

9 (9 x + 2 y) - 9 (9 x - 2 y) : 36 y

= \frac{36 y}{( 9 x + 2 y ) ^{2}}

d er i v a t i v e f (x) = \frac{x ^{\frac{1}{3}} - 4}{x ^{\frac{7}{2}}}

d er i v a t i v e \frac{3}{4} s^{2}

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

z \to 1 + i lim (z^{2} + i)

\int (3 x - 5)^{4} d x