(\partial)/(\partial x)(5/(5x+3y))

解答

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

- \frac{25}{( 5 x + 3 y ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

将

y

视为常数

将常数提出:

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

= 5 \frac{\partial}{\partial x} (\frac{1}{5 x + 3 y})

使用指数法则:

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

= 5 \frac{\partial}{\partial x} ((5 x + 3 y)^{- 1})

使用连锁律:

- \frac{1}{( 5 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (5 x + 3 y)

= - \frac{1}{( 5 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (5 x + 3 y)

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= 5 (- \frac{1}{( 5 x + 3 y ) ^{2}} \cdot 5)

化简

5 (- \frac{1}{( 5 x + 3 y ) ^{2}} \cdot 5) : - \frac{25}{( 5 x + 3 y ) ^{2}}

= - \frac{25}{( 5 x + 3 y ) ^{2}}

in v erse l a pl a ce \frac{10}{s ( s + 2 ) ( s + 3 ) ^{2}}

x \to 0 - lim (x sin (\frac{1}{x}))

x y^{^{'}} + y = - 5 x y^{2}, y (1) = 7

\int arccot (2 y) d y

y^{^{'}} = \frac{x y ^{3}}{16}