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

解答

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

- \frac{2 x}{y ^{3}}

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x (- 2 y^{- 2 - 1})

化简

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

= - \frac{2 x}{y ^{3}}

x \to 0 lim (\frac{7}{1 + x})

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

\int (\frac{2 x ^{3} + 10 x ^{2} + 8 x - 12}{4 x}) d x

\int \frac{x}{x ^{2} + 9} d x

y^{^{'''}} + 2 y^{^{''}} - 10 y^{^{'}} - 20 y = 0