(\partial)/(\partial y)(xy+2/x+4/y)

解

\frac{\partial}{\partial y} (x y + \frac{2}{x} + \frac{4}{y})

x - \frac{4}{y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (x y + \frac{2}{x} + \frac{4}{y})

x

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 y} (x y) + \frac{\partial}{\partial y} (\frac{2}{x}) + \frac{\partial}{\partial y} (\frac{4}{y})

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

\frac{\partial}{\partial y} (\frac{2}{x}) = 0

\frac{\partial}{\partial y} (\frac{4}{y}) = - \frac{4}{y ^{2}}

= x + 0 - \frac{4}{y ^{2}}

簡素化

= x - \frac{4}{y ^{2}}