Notes On Second Order Derivatives - CBSE Class 12 Maths

Consider a function y = f(x) (the derivative of y with respect to x)

dy/dx = f '(x)

d/dx(dy/dx) is called the second order derivative of y w.r.t. x.

d/dx(dy/dx) = d2y/dx2 or D2y or y'' or y2

d/dx(f '(x)) = f '' (x)

Third order derivative of y w.r.t. x = d3y/dx3

Fourth order derivative of y w.r.t. x = d4y/dx4

Summary

Consider a function y = f(x) (the derivative of y with respect to x)

dy/dx = f '(x)

d/dx(dy/dx) is called the second order derivative of y w.r.t. x.

d/dx(dy/dx) = d2y/dx2 or D2y or y'' or y2

d/dx(f '(x)) = f '' (x)

Third order derivative of y w.r.t. x = d3y/dx3

Fourth order derivative of y w.r.t. x = d4y/dx4

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