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The sum rule states that
\begin{equation*} \DDX\left[f(x)+g(x)\right] = f'(x) + g'(x) \end{equation*}
See the proof of the sum rule.
\begin{eqnarray*} \DDX(x + 1) & = & \DDX x + \DDX 1 = 1 \\ \DDX(x^2 - 3x + 2) & = & \DDX x^2 + \DDX(-3x) + \DDX(2) = 2x-3 \\ \DDX(\sin x + \cos x) & = & \DDX\sin x + \DDX\cos x = \cos x - \sin x \end{eqnarray*}
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This is version 5 of sum rule, born on 2002-02-24, modified 2004-03-22.
Object id is 2637, canonical name is SumRule.
Accessed 7771 times total.
Classification:
| AMS MSC: | 26A24 (Real functions :: Functions of one variable :: Differentiation : general theory, generalized derivatives, mean-value theorems) |
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Pending Errata and Addenda
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