(\partial)/(\partial x)((x^{0.5}+y^{0.5})^2)

解

\frac{\partial}{\partial x} ((x^{0.5} + y^{0.5})^{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^{0.5} + y^{0.5})^{2})

y

を定数として扱う

連鎖法則を適用:

2 (x^{0.5} + y^{0.5}) \frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

= 2 (x^{0.5} + y^{0.5}) \frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

\frac{\partial}{\partial x} (x^{0.5} + y^{0.5}) = \frac{0.5}{x ^{\frac{1}{2}}}

= 2 (x^{0.5} + y^{0.5}) \frac{0.5}{x ^{\frac{1}{2}}}

簡素化

2 (x^{\frac{1}{2}} + y^{\frac{1}{2}}) \frac{0.5}{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}}}