(\partial)/(\partial y)(-1/(ln(10)(x-y)))

解答

\frac{\partial}{\partial y} (- \frac{1}{ln ( 10 ) ( x - y )})

- \frac{1}{ln ( 10 ) ( x - y ) ^{2}}

求解步骤

\frac{\partial}{\partial y} (- \frac{1}{ln ( 10 ) ( x - y )})

将

x

视为常数

将常数提出:

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

= - \frac{1}{ln ( 10 )} \frac{\partial}{\partial y} (\frac{1}{x - y})

使用指数法则:

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

= - \frac{1}{ln ( 10 )} \frac{\partial}{\partial y} ((x - y)^{- 1})

使用连锁律:

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

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

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

= - \frac{1}{ln ( 10 )} (- \frac{1}{( x - y ) ^{2}} (- 1))

化简

- \frac{1}{ln ( 10 )} (- \frac{1}{( x - y ) ^{2}} (- 1)) : - \frac{1}{ln ( 10 ) ( x - y ) ^{2}}

= - \frac{1}{ln ( 10 ) ( x - y ) ^{2}}

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