Find all functions having a derivative y = x2-3x.

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

Let’s use the basic rules and formulas for differentiation:

(x ^ n) ‘= n * x ^ (n-1).

(c) ‘= 0, where c is const.

(c * u) ’= c * u’, where c is const.

(u ± v) ‘= u’ ± v ‘.

(uv) ‘= u’v + uv’.

y = f (g (x)), y ’= f’u (u) * g’x (x), where u = g (x).

That is, the derivative of our given function will be as follows:

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

Answer: The derivative of our given function is f (x) ‘= 2x – 3.