Find the value of the derivative of the function y = f (x) at the point x0, if f (x) = sin x, x0 = -π / 4.

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

Using the basic formulas and rules of differentiation:

(x ^ n) ‘= n * x ^ (n-1).

(sin x) ’= cos x.

(cos x) ‘= -sin x.

(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) ‘= (3cos (x) – sin (x))’ = (3cos (x))) ‘- (sin (x))’ = -3sin (x) – cos (x).

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

f (x) ‘(pi) = -3sin (pi) – cos (pi) = -3 * 0 – (-1) = 0 + 1 = 1.

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