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

解答

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

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

求解步骤

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

将

x, y

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

l a pl a ce t r an s f or m 4 sin (π t)

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