for the derivatives of a product
A formula that gives an expression for the $n$-th derivative of the product of two functions in terms of their derivatives of orders $k=0,\dots,n$ (the derivative of order zero is understood to be the function itself). Namely, if the functions $u=u(x)$ and $v=v(x)$ have derivatives up to the order $s$ inclusive at some point, then at this point their product $uv$ has derivatives of the same orders, and for $n=0,\dots,s$,
This formula was communicated by G. Leibniz in a letter to J. Bernoulli in 1695.
Leibniz formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Leibniz_formula&oldid=33308