(\partial)/(\partial x)(1/({f)(x)})

解

\frac{\partial}{\partial x} (\frac{1}{f ( x )})

- \frac{\frac{\partial}{\partial x} ( f ( x ) )}{f ( x ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{1}{f ( x )})

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

簡素化

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

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