Both Newton and Liebniz had access to Barrow's work and to that of Fermat. The fact that finding areas and tangents were inverse operationa had been know for some time. What Newton and Liebniz did was to produce a coherent set of formulae to unify what was a hodge-podge collection of procedures. Newton's methods were clumsy and the Leibniz formulation is what is generally used now. Boyer points out that the calculus was "in the air" at the time.
I am sure it was in the air. Read recently about the discovery of DNA which was also 'in the air' at the time and was a race between Watson and Crick and Linus Pauling. There comes a time when technology, knowledge and need allow certain discoveries.