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

解答

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

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

求解步骤

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

将

y, z

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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