Find the third derivative of the function f(x) = 5x4 + 4x3 - 7x2.
We'll find each derivative along the way. The first derivative is
f (1)(x) = 20x3 + 12x2 - 7x.
We take another derivative to find the second derivative of f :
f (2)(x) = 60x2 + 24x - 7.
Finally, one more time to find the third derivative of f:
f (3)(x) = 120x + 24.