Leibniz was a great philosopher in the 17th century. He published his calculus research results before Newton. But at that time Newton published his personal notes, indicating that he has used the principle of calculus at least 10 years before Leibniz published his results. Newton also said that shortly before Leibniz published his results, he talked about his thoughts on calculus in a letter to Leibniz. However, the research afterwards showed that in Newton's letter, the few lines about calculus hardly involve any important aspects of this theory. 
There is no a third person independently invented calculus no later than Leibniz and Newton
 it can be concluded that Leibniz and Newton independently published calculus.