How to find the second derivative of a function: definition, 1 example, and its solution.
The second derivative is the derivative of a derivative.
So, to find the second derivative,
differentiate the function [twice].
It is written as f''(x), y'', d2y/dx2, (d2/dx)f(x).
Exampley = x5 - 7x2 - 8x + 1, f''(x) = ?
First find the derivative f'(x).
f(x) = x5 - 7x2 - 8x + 1.
Then f'(x) = 5x4 - 7⋅2x1 - 8 + 0.
Derivative of a Polynomial
-7⋅2x1 = -14x
f'(x) = 5x4 - 14x - 8.
To find f''(x), differentiate again:
find the derivative of f'(x).
Then f''(x) = 5⋅4x3 - 14 - 0.
5⋅4x3 = 20x3
So f''(x) = 20x3 - 14.