(\partial)/(\partial x)(9/x+3/y+xy)

解

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

y - \frac{9}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

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} (\frac{9}{x}) + \frac{\partial}{\partial x} (\frac{3}{y}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

\frac{\partial}{\partial x} (\frac{3}{y}) = 0

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

= - \frac{9}{x ^{2}} + 0 + y

簡素化

= y - \frac{9}{x ^{2}}