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

解答

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

- \frac{9}{( 3 x + y ) ^{2}}

求解步骤

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

将

y

视为常数

将常数提出:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{3 x + y})

使用指数法则:

\frac{1}{a} = a^{- 1}

= 3 \frac{\partial}{\partial x} ((3 x + y)^{- 1})

使用连锁律:

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

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

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

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

化简

3 (- \frac{1}{( 3 x + y ) ^{2}} \cdot 3) : - \frac{9}{( 3 x + y ) ^{2}}

= - \frac{9}{( 3 x + y ) ^{2}}

\int - \frac{1}{2} y d y

x \to - 1 lim (x + 3)

in v erse l a pl a ce \frac{0.6}{s + 2}

\frac{d y}{d x} = \frac{( x ^{2} y - y )}{( y + 1 )}, y (0) = 1

\int e^{u} d u