Differential calculus is one of the two traditional sub-disciplines of the calculus which is used to study the rates of changes in the quantities. It studies the derivatives of a function and its relations, in which the chosen input value describes the rate of changes of the function. This process of finding a derivative of a function is known as differentiation and differential calculus is used to calculate the differentiation. As well as integral calculus, differential calculus is based on fundamental theorem of calculus is the reverse process of integral calculus.
Differential calculus is an ancient mathematics and its concept can be find in work of Euclid (300 BCE) and Archimedes (287 BCE), likewise it was developed in India by Aryabhatta (476-550) who used infinitesimals to study the accurate motion of the moon. It was also enriched by Persian mathematician Sharaf al-Din-al-Tosi (1135-1213) who discovered the derivatives of cubic polynomials and other mathematicians. In modern time Isaac Newton and Gottfried Leibniz worked in differential calculus and used it in general mathematics to find the solution of complex problems.
Fundamental theorems of differential calculus are based on function and its derivatives and it is used to describe the differential equations. It is a must have tool of science and engineering subjects such as physics, chemistry, geology, pharmacy, astronomy, etc. Main topics of differential calculus are Calculus with polynomials, Chain rule, Constant factor rule in differentiation, Derivative, Derivative (examples), Derivative of a constant, Differential (calculus), Differential equation, Differential operator, Extreme value theorem, First derivative test, Implicit differentiation, Inverse functions and differentiation, Leibniz’s notation for differentiation, Leibniz’s rule, L’Hôpital’s rule, Linearity of differentiation, Logarithmic derivative, Maxima and minima, Mean value theorem, Newton’s method, Newton’s notation for differentiation, Notations , Product rule, Quotient rule, Regiomontanus’ angle maximization problem, Related rates, Second derivative test, Simplest rules, Stationary point, Sum rule in differentiation, Taylor’s theorem.