(\partial)/(\partial x)(1/y-1/(x^2))

解

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

\frac{2}{x ^{3}}

解答ステップ

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

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

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

= 0 - (- \frac{2}{x ^{3}})

簡素化

= \frac{2}{x ^{3}}