In the manuscript "Determinationum progressio in infinitum" (pp. 668-675 of Sämtliche Schriften und Briefe, Reihe VII, Band 3, Teil C, available in pdf here), Leibniz writes on p. 673 (with "$\sqcap$" in place of "$=$"):
$$ \odot = \overline{dt}\int\frac{a^2}{a^2 + t^2}. \quad\text{Hence}\quad \overline{d\odot} = \frac{a^2}{a^2 + t^2}\overline{d\overline{dt}} $$
This amounts to asserting that $d[uv] = dv\,du$ where $u=dt$ and $v=\int\frac{a^2}{a^2+t^2}$; and thus differentiating the product wrong, as the editors comment in footnote 14. On p. 668 they take this as grounds to date the manuscript early November 1675, since by November 11 he had corrected this (in "Methodi tangentium inversae exempla", quoted by Edwards in KConrad's comment above).