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

解

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

\frac{0.5}{x ^{\frac{1}{2}}}

解答ステップ

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

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (x^{0.5}) = \frac{0.5}{x ^{0.5}}

\frac{\partial}{\partial x} (y^{0.5}) = 0

= \frac{0.5}{x ^{0.5}} + 0

簡素化

= \frac{0.5}{x ^{\frac{1}{2}}}