Find the value of the derivative of the function at the point y = 3cosx-sinx, x0 = pi.
September 1, 2021 | education
| 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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.