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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