(\partial)/(\partial x)((1/x+1/y)^{-1})

解答

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

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

求解步骤

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

将

y

视为常数

使用连锁律:

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

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

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

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

化简

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

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

cos (x) \frac{d y}{d x} + sin (x) y = 1

\int x^{3} - \frac{1}{2} d x

\int x \cdot cos (\frac{π x}{2}) d x

\frac{d}{d x} (\frac{x - 6}{3 - 4 x})

x \to - 3 lim (9)