(\partial)/(\partial x)((7y-4x)/(y^2+2x^2))

解答

\frac{\partial}{\partial x} (\frac{7 y - 4 x}{y ^{2} + 2 x ^{2}})

\frac{8 x ^{2} - 28 y x - 4 y ^{2}}{( y ^{2} + 2 x ^{2} ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{7 y - 4 x}{y ^{2} + 2 x ^{2}})

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} ( 7 y - 4 x ) ( y ^{2} + 2 x ^{2} ) - \frac{\partial}{\partial x} ( y ^{2} + 2 x ^{2} ) ( 7 y - 4 x )}{( y ^{2} + 2 x ^{2} ) ^{2}}

\frac{\partial}{\partial x} (7 y - 4 x) = - 4

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

= \frac{( - 4 ) ( y ^{2} + 2 x ^{2} ) - 4 x ( 7 y - 4 x )}{( y ^{2} + 2 x ^{2} ) ^{2}}

化简

\frac{( - 4 ) ( y ^{2} + 2 x ^{2} ) - 4 x ( 7 y - 4 x )}{( y ^{2} + 2 x ^{2} ) ^{2}} : \frac{8 x ^{2} - 28 y x - 4 y ^{2}}{( y ^{2} + 2 x ^{2} ) ^{2}}

= \frac{8 x ^{2} - 28 y x - 4 y ^{2}}{( y ^{2} + 2 x ^{2} ) ^{2}}

\frac{d}{d x} (30 x)

\int (x^{8} - 4 x^{2})^{3} (x^{7} - x) d x

\frac{\partial}{\partial z} (x e^{y})

d er i v a t i v e y = \frac{1}{2 x + 7}

d er i v a t i v e f (x) = 2 x + \frac{5}{x}