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

解答

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

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

求解步骤

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

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

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

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

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

化简

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

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

\int \frac{64 x ^{2}}{x ^{4} - 40 x ^{2} + 144} d x

\int 3 sec^{3} (x) d x

d er i v a t i v e - 7 x^{\frac{2}{3}} - 2 + 3 x^{\frac{7}{4}}

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

d er i v a t i v e f (x) = 2 x^{2} - 196 ln (x)