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

解答

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

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

求解步骤

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

将

x

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= 2 x^{2} \frac{1 \cdot ( 3 + x ^{2} y ^{2} ) - 2 x ^{2} yy}{( 3 + x ^{2} y ^{2} ) ^{2}}

化简

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

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

\int \frac{e ^{t}}{1 + e ^{t}} d t

n = 0 \sum \infty (0.5)^{n}

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

(1 + x^{2}) d y - (1 + 4 y^{2}) d x = 0

n = 1 \sum \infty \frac{( 1 )}{2 n + 1}