Find the Derivative of the Function: f (x) = x³-2x² + 5

Let’s find the derivative of our given function: f (x) = x ^ 3 – 2x ^ 2 + 5.

Using the basic differentiation formulas and differentiation rules:

(x ^ n) ‘= n * x ^ (n – 1).
(c) ‘= 0, where c is const.
(c * u) ’= c * u’, where c is const.
(u + v) ‘= u’ + v ‘.
Thus, the derivative of our given function will be as follows:

f (x) ‘= (x ^ 3 – 2x ^ 2 + 5)’ = (x ^ 3) ‘- (2x ^ 2)’ + (5) ‘= 3 * x ^ (3 – 1) – 2 * 2 * x ^ (2 – 1) +0 = 3 * x ^ 2 – 4 * x ^ 1 = 3x ^ 2 – 4x.

Answer: The derivative of our given function will be equal to f (x) ‘= 3x ^ 2 – 4x.