(\partial)/(\partial x)((y^2)/(4-x^2))

解

\frac{\partial}{\partial x} (\frac{y ^{2}}{4 - x ^{2}})

\frac{2 y ^{2} x}{( 4 - x ^{2} ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{y ^{2}}{4 - x ^{2}})

y

を定数として扱う

定数を除去:

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

= y^{2} \frac{\partial}{\partial x} (\frac{1}{4 - x ^{2}})

指数の規則を適用する:

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

= y^{2} \frac{\partial}{\partial x} ((4 - x^{2})^{- 1})

連鎖法則を適用:

- \frac{1}{( 4 - x ^{2} ) ^{2}} \frac{\partial}{\partial x} (4 - x^{2})

= - \frac{1}{( 4 - x ^{2} ) ^{2}} \frac{\partial}{\partial x} (4 - x^{2})

\frac{\partial}{\partial x} (4 - x^{2}) = - 2 x

= y^{2} (- \frac{1}{( 4 - x ^{2} ) ^{2}} (- 2 x))

簡素化

y^{2} (- \frac{1}{( 4 - x ^{2} ) ^{2}} (- 2 x)) : \frac{2 y ^{2} x}{( 4 - x ^{2} ) ^{2}}

= \frac{2 y ^{2} x}{( 4 - x ^{2} ) ^{2}}