Product rule

Gottfried Wilhelm Leibniz, um 1700, Öl auf Holz
Gottfried Wilhelm Leibniz, um 1700, Öl auf Holz (Photo credit: Wikipedia)

And here’s a quick recap of a demonstration of the product rule (after Leibniz):

\frac{d}{dx}(u(x)v(x)) = (u(x) + \frac{du}{dx})(v(x) + \frac{dv}{dx}) - u(x)x(x)

= u(x)v(x) - u(x)v(x) + u(x)\frac{dv}{dx} + v(x)\frac{du}{dx}

Which is, of course, the product rule.

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