(\partial)/(\partial x)(e^{(xy)^{1/2}})

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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