(\partial)/(\partial x)(1/x+1/y)

解答

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

- \frac{1}{x ^{2}}

求解步骤

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

将

y

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

= - \frac{1}{x ^{2}} + 0

化简

= - \frac{1}{x ^{2}}

\frac{d}{d x} ((4 - x^{\frac{2}{3}})^{\frac{3}{2}})

ma c l a u r in e^{- 3 x^{2}}

x \to 6 lim (f (x) - g (x))

\frac{d ^{2}}{d x ^{2}} (6 cos (3 x + 3))

in v erse l a pl a ce \frac{1}{s ^{2} - 4}