(\partial)/(\partial y)((x)(1+2xsqrt(y)))

解

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

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

解答ステップ

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

x

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial y} (1) = 0

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

= x (0 + \frac{x}{y})

簡素化

x (0 + \frac{x}{y}) : \frac{x ^{2}}{y}

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