(\partial)/(\partial x)(1/(2+xy^2))

解

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

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

解答ステップ

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

y

を定数として扱う

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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