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

解

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

- \frac{y ^{\frac{1}{2}}}{4 π x ^{\frac{3}{2}}}

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 π} \cdot \frac{1}{2 ( \frac{y}{x} ) ^{\frac{1}{2}}} (- \frac{y}{x ^{2}}) : - \frac{y ^{\frac{1}{2}}}{4 π x ^{\frac{3}{2}}}

= - \frac{y ^{\frac{1}{2}}}{4 π x ^{\frac{3}{2}}}