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

解

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

\frac{x ^{\frac{1}{2}} + y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{x ^{\frac{1}{2}} + y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}