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

解

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

- \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (x^{2} + y^{2})

= - \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (x^{2} + y^{2})

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

= - \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \cdot 2 x

簡素化

- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \cdot 2 x : - \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

= - \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}