# Product rule

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.