(\partial)/(\partial x)(x/(y^2)-y/(x^2))

解

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} - \frac{y}{x ^{2}})

\frac{1}{y ^{2}} + \frac{2 y}{x ^{3}}

解答ステップ

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} - \frac{y}{x ^{2}})

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{x}{y ^{2}}) - \frac{\partial}{\partial x} (\frac{y}{x ^{2}})

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

\frac{\partial}{\partial x} (\frac{y}{x ^{2}}) = - \frac{2 y}{x ^{3}}

= \frac{1}{y ^{2}} - (- \frac{2 y}{x ^{3}})

簡素化

= \frac{1}{y ^{2}} + \frac{2 y}{x ^{3}}