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

解

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

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

解答ステップ

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

z, x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial w} (z) = 0

\frac{\partial}{\partial w} (w) = 1

= x^{\frac{1}{2}} (0 + 1)

簡素化

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