The mathematical study of change like motion, growth or decay is calculus. The Rate of change of given function is derivative or differential. The concept of derivative is essential in day to day life. Also applicable in Engineering, Science, Economics, Medicine etc.
Let y = f (x) --(1) be a real valued function.The first order derivative of y denoted by or y’ or y1 or∆1. The Second order derivative of y denoted by or y’’ or y2 or ∆2. Similarly differentiating the function (1) n-times, successively, the nthorder derivative of y exists denoted by or yn or yn or ∆n. The process of finding 2nd and higher order derivatives is known as Successive Differentiation.
nthderivative of some standard functions:
1. y = eax
Solutions: y1 = a eax
y2 = a2 eax
Differentiate Successively we get;
yn = an eax
Case -1 If m = n in (*)
Case -2 If m > n in (*)