Who developed calculus independently of Newton?

Leibniz, and the priority dispute that followed is one of the ugliest in the history of science. Newton developed his version first, around 1666, and did not publish; Leibniz developed his independently in the 1670s and published first, in 1684.

Newton then used his position to destroy him. As president of the Royal Society he appointed a committee to adjudicate the dispute, packed it, and wrote its supposedly impartial report himself - then wrote an anonymous review of that report, also himself. Leibniz died in 1716 in disfavour, and his funeral was attended by his secretary.

Leibniz's notation won completely. The dy/dx and the elongated S for an integral are his, chosen because they make the structure of the operations visible; Newton's dot notation is clumsier and English mathematics used it out of loyalty for a century, falling behind the continent as a direct result. He also built a mechanical calculator that could multiply, described binary arithmetic, and worked on a universal formal language for reasoning - which makes him a plausible ancestor of computing as well as of half of calculus.