What is the meaning of double derivative?

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We'll discuss the meaning of double derivative on an example.
We'll take the function: f(x)= x^3 + 2x^2 - 32x
First, we'll take the derivative of the function f(x) = y and then we'll take the derivative of the resulting function f'(x) = y’.Then it is called the double derivative.
Let differentiate f(x)= x^3 + 2x^2 - 32x, with respect to x, to get f ' (x):

f '(x) = 3x^2 + 2*2x - 32.

f '(x) = 3x^2 + 4x - 32

We'll differentiate again the result f'(x), with respect to x and we'll get f "(x):

f "(x) = 6x+ 4.

**Therefore, the double derivative is: f "(x) = 6x + 4.**

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