(\partial)/(\partial x)(xc^2(1/(sqrt(1-\frac{v^2){c^2)}}-1))

解

\frac{\partial}{\partial x} x c^{2} \frac{1}{1 - \frac{v ^{2}}{c ^{2}}} - 1

c^{2} (\frac{c}{c ^{2} - v ^{2}} - 1)

解答ステップ

\frac{\partial}{\partial x} x c^{2} \frac{1}{1 - \frac{v ^{2}}{c ^{2}}} - 1

簡素化

x c^{2} \frac{1}{1 - \frac{v ^{2}}{c ^{2}}} - 1 : c^{2} x (\frac{c ^{2}}{c ^{2} - v ^{2}} - 1)

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

c, v

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

共通の導関数を適用:

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

= c^{2} (\frac{c ^{2}}{c ^{2} - v ^{2}} - 1) \cdot 1

簡素化

c^{2} (\frac{c ^{2}}{c ^{2} - v ^{2}} - 1) \cdot 1 : c^{2} (\frac{c}{c ^{2} - v ^{2}} - 1)

= c^{2} (\frac{c}{c ^{2} - v ^{2}} - 1)