Bhāskara II described 'instantaneous motion' and ideas close to the derivative — five centuries before Newton and Leibniz.
In the Siddhānta Śiromaṇi, Bhāskara II uses tātkālika gati (instantaneous velocity) for planetary motion, anticipating ideas related to Rolle's theorem and d(sin)/dθ ≈ cos.
— Bhāskara II, Siddhānta Śiromaṇi (1150 CE)
Differential calculus (Newton & Leibniz, late 17th c.).
A genuine, defensible parallel.
Bhāskara II needed to compute where a planet is moving fastest, and to do it he reasoned about motion over a vanishingly small interval — the core intuition behind the derivative. He stated that a planet's instantaneous velocity relates to the change in position, anticipated what we call Rolle's theorem, and knew the derivative of sine behaves like cosine.
The honest boundary: these are brilliant, specific results, not a general theory of calculus with limits and the fundamental theorem — that synthesis was Newton and Leibniz's. Together with the later Kerala school's infinite series, though, India clearly developed substantial pre-calculus analysis, and Bhāskara's instantaneous-motion idea is a genuine landmark.