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Both of them came up with the concept (semi-) independently; both were aware that the other was working on it and in fact they exchanged letters on the subject, but they approached it from different directions (Newton started with differentiation, Leibniz started with integration).

Going by their private papers it appears that Newton was further along earlier than Leibniz, but Leibniz published a full description much earlier than Newton did.

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Q: Who is the father of calculus Newton or Leibniz?
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