Use of the concept of derivative in the computation of vyatīpāta in two Kerala texts

It is well known that the concept of derivative was used in finding the rates of motion of planets in Indian astronomy texts beginning with Laghumānasa (c. 932 CE). In his Vāsanābhāṣya of his own work, Siddhāntaśiromaṇi (c.1150 CE), Bhāskarācārya explains the necessity of using the concept of tātkālikagati (instantaneous rates of motion) of planets, which involves using the derivative of the sine function, and discusses the retrograde motion of planets also, using the concept. Later, Kerala texts like Tantrasaṅgraha also discuss this concept. In two Kerala texts, Karaṇottama of Acyuta Piṣāraṭi (late sixteenth century) and Dṛkkaraṇa (1608 CE), the use of the concept of derivative is used in a very different context, namely, computations pertaining to vyatīpāta. In this paper, we describe the algorithms involving the ‘krāntigati’ or the rate of change of the declinations of the Sun and the Moon involving the derivative conept, in these two texts.