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(view preamble)
Cross-references: equality, sum, limit, line, argument, domain, derivative, differentiable, product, differentiable functions
There is 1 reference to this entry.
This is version 3 of proof of product rule, born on 2002-02-24, modified 2004-10-15.
Object id is 2629, canonical name is ProofOfProductRule.
Accessed 11597 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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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
![$\displaystyle \frac{\ensuremath{\mathrm{d}}}{\ensuremath{\mathrm{d}x}}\left[f(x)g(x)\right]$](http://images.planetmath.org:8080/cache/objects/2629/l2h/img6.png "$\displaystyle \frac{\ensuremath{\mathrm{d}}}{\ensuremath{\mathrm{d}x}}\left[f(x)g(x)\right]$")
![$\displaystyle \lim_{h\to0}\left[f(x+h)\frac{g(x+h)-g(x)}{h} + g(x)\frac{f(x+h)-f(x)}{h}\right]$](http://images.planetmath.org:8080/cache/objects/2629/l2h/img12.png "$\displaystyle \lim_{h\to0}\left[f(x+h)\frac{g(x+h)-g(x)}{h} + g(x)\frac{f(x+h)-f(x)}{h}\right]$")
![$\displaystyle \lim_{h\to0}\left[f(x+h)\frac{g(x+h)-g(x)}{h}\right] + \lim_{h\to0}\left[g(x)\frac{f(x+h)-f(x)}{h}\right]$](http://images.planetmath.org:8080/cache/objects/2629/l2h/img14.png "$\displaystyle \lim_{h\to0}\left[f(x+h)\frac{g(x+h)-g(x)}{h}\right] + \lim_{h\to0}\left[g(x)\frac{f(x+h)-f(x)}{h}\right]$")
