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

解答

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

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

求解步骤

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

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

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

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

化简

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

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

\frac{d}{d x} (\frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )})

d er i v a t i v e \frac{9}{x - 6}

\int_{1}^{5} 1 + (4)^{2} d x

\frac{d}{d x} (\frac{3}{2 x})

x \to 1 lim (- 3 a x + b)