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Second Order Derivative

notes

Let y = f(x). Then
(dy)/(dx) = f'(x)  ... (1)
If f′(x) is differentiable, we may differentiate (1) again w.r.t. x. Then, the left hand side becomes d/(dx)((dy)/(dx))  which is called the second order derivative of y  w.r.t. x and is denoted by (d^2y)/(dx^2).
The second order derivative of f(x) is denoted by f″(x). It is also denoted by D^2 y or y″ or y_2 if y = f(x).
We remark that higher order derivatives may be defined similarly.

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Continuity and Differentiability part 35 (Example Second Order Derivative) [00:14:22]
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