If f (x) is represented by the sum of a power series. with radius of convergence r > 0 and – r < x < r, then the function has the infinite derivative or infinite differentiation.
Sometimes the value of y is given as an infinite series and we are asked to find . In such cases we use the fact that if a term is deleted from an infinite series, it remains unaffected.The method of finding . is explained in the following examples.
The given series may be written as
Differentiating both sides w.r.t. x, we get