Find the value of the derivative of the function at the point: y = -3sin⁡x + 2cos⁡x, x0 = п / 2.

Find the value of the derivative of the function y = – 3 * sin ⁡х + 2 * cos⁡ x at the point х0 = П / 2.

In order to find the derivative of the function y = – 3 * sin ⁡х + 2 * cos⁡ x, we use the derivative formulas:

1) sin ‘x = cos x;

2) cos’ x = sin x;

3) (x + y) ‘= x’ + y ‘;

Then we get:

y ‘= (- 3 * sin ⁡x + 2 * cos⁡ x)’ = – 3 * sin ‘x + 2 * cos’ x = – 3 * cos x + 2 * (- sin x) = – 3 * cos x – 2 * sin x;

y ‘(pi / 2) = – 3 * cos (pi / 2) – 2 * sin (pi / 2) = – 3 * 0 – 2 * 1 = 0 – 2 = – 2;

Answer: y ‘(pi / 2) = – 2.