Find the derivative of the function y = (a + x / a-x) ^ k

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

This function can be written like this: f (x) = x ^ 2 – 6x + 9 + x = x ^ 2 – 5x + 9.

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 ‘.

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

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

f (x) ‘= (x ^ 2 – 5x + 9)’ = (x ^ 2) ‘- (5x)’ + (9) ‘= 2 * x ^ (2 – 1) – 5 * x ^ (1 – 1) – 0 = 2x – 5.

We calculate the value of the derivative at the point x0 = 3:

f (x) ‘(3) = 2 * 3 – 5 = 6 – 5 = 1.

Answer: The derivative of our given function will be equal to f (x) ‘= 2x – 5, and f (x)’ (3) = 1.