(\partial)/(\partial x)(1+c/x-b/(x^3))

解

\frac{\partial}{\partial x} (1 + \frac{c}{x} - \frac{b}{x ^{3}})

\frac{3 b}{x ^{4}} - \frac{c}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (1 + \frac{c}{x} - \frac{b}{x ^{3}})

c, b

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} (1) + \frac{\partial}{\partial x} (\frac{c}{x}) - \frac{\partial}{\partial x} (\frac{b}{x ^{3}})

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

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

\frac{\partial}{\partial x} (\frac{b}{x ^{3}}) = - \frac{3 b}{x ^{4}}

= 0 - \frac{c}{x ^{2}} - (- \frac{3 b}{x ^{4}})

簡素化

= \frac{3 b}{x ^{4}} - \frac{c}{x ^{2}}