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

解

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

\frac{2 e ^{- \frac{2 y}{x}} y}{x ^{2}}

解答ステップ

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

簡素化

e^{\frac{- 2 y}{x}} : e^{- \frac{2 y}{x}}

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

= e^{- \frac{2 y}{x}} \frac{2 y}{x ^{2}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{- \frac{2 y}{x}} y}{x ^{2}}