(\partial)/(\partial m)(mc^2(1/(sqrt(1-\frac{v^2){c^2)}}-1))

解答

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

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

求解步骤

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

化简

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

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

将

c, v

视为常数

将常数提出:

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

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

使用常见微分定则:

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

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

化简

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)

x \to \infty lim (\frac{3 ^{x} + 2 ^{x}}{3 ^{x + 1} + 2 ^{x - 1}})

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