A couple of posts ([\[1\]][1], [\[2\]][2]) on matheducators.SE seem to suggest that Leibniz originally got the wrong form for the product rule, perhaps thinking that $(fg)'=f'g'$. Is there any actual historical evidence for this?

It seems particularly hard to believe that he would have made the hypothesis $(fg)'=f'g'$. We would then have $x'=(1x)'=(1')(x')=0$. And presumably anyone inventing calculus would take $(x^2)'$ to be a prototypical problem, and would realize pretty early on that $(x^2)'\ne (x')(x')=1$. It's also pretty trivial to disprove this conjecture based on dimensional analysis or scaling.

There is some discussion on [this][3] Wikipedia talk page, with some sources cited, but it appears to be inconclusive.

  [1]: https://matheducators.stackexchange.com/a/4419/507
  [2]: https://matheducators.stackexchange.com/a/4417/507
  [3]: http://en.wikipedia.org/wiki/Talk%3AProduct_rule#Leibniz_did_not_make_this_error