Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 13/Differentials
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Differentials
Let $y = \map f x$ and $\Delta y = \map f {x + \Delta x} - \map f x$. Then:
where $\epsilon \to 0$ as $\Delta x \to 0$. Thus:
- $13.50$: $\Delta y = \map {f'} x \Delta x + \epsilon \Delta x$
If we call $\Delta x = \d x$ the differential of $x$, then we define the differential of $y$ to be: