Find the tangent of the angle alpha between the tangent to the graph of the function y = 3 ctg x at the point with the abscissa

Find the tangent of the angle alpha between the tangent to the graph of the function y = 3 ctg x at the point with the abscissa x0 = P / 3 and the positive direction of the Ox axis.

The slope of the tangent or the tangent of the angle of inclination of the tangent drawn to the graph of the function to the positive direction of the abscissa axis is equal to the value of the drive function calculated at the point of tangency.

Therefore, in order to find out the angle of inclination of the tangent drawn to the graph of the function y = 3ctgx at the point with the abscissa x0 = π / 3, we need to find the derivative of the function y = 3ctgx and calculate the value of this derivative at the point x0 = π / 3:

y ‘(x) = (3ctgx)’ = 3 * (ctgx) ‘= 3 * (-1 / sn ^ 2x)’ = -3 / sn ^ 2x.

Find y ‘(π / 3):

y ‘(π / 3) = -3 / sn ^ 2 (π / 3) = -3 / (√3 / 2) ^ 2 = -3 / (3/4) = -4.