(\partial)/(\partial z)(1/(xy^2z))

解答

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

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

求解步骤

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

将

x, y

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

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

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

化简

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

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