Chapter 4: Successive Differentiation
Return to Table of Content Successive Differentiation Let be a function of the derivative or Differential coefficient of w.r.t. is denoted by Where Similarly the second order derivative of y w.r.t. x is defined as Similarly we get nth derivative or Differential coefficient of w.r.t. and is denoted by Application: 1. Series expansion of a function like Taylor’s and McLaurin's series expansion. 2. Solution of ordinary and partial differential equations. Ex. Using Taylor’s Series Example 1: Find the nth derivative of Solution: differentiating y w.r.t. x we get, …….......(1) Differentiating again w.r.t. x, we get …….......(2) Similarly differentiating successively, we get …….......(3) .......(4) … … … … … ...