(\partial)/(\partial x)(((yx)/(zw))^{1/2})

解

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

\frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

解答ステップ

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

y, z, w

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (\frac{y x}{z w}) = \frac{y}{z w}

= \frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \cdot \frac{y}{z w}

簡素化

\frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \cdot \frac{y}{z w} : \frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

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