Question

F(x)=cosx-sinП/3x0=П/2вычислите значение производной данной функции в точке x0​

Answer 1

Ответ:

Объяснение:

f'(x)=-sinx,  f'(p/2)=-sin(p/2)=-1,    (sinp/3 - постоянная величина,

от нее производная =0)

Answer 2

To find the derivative of the function f(x) = cos(x) - sin(π/3)x, we can apply the rules of differentiation.

The derivative of cos(x) is -sin(x), and the derivative of sin(π/3)x is π/3*cos(π/3)x.

Therefore, the derivative of f(x) is given by:

f'(x) = -sin(x) - π/3*cos(π/3)x

To find the value of the derivative at x0 = π/2, we substitute π/2 into the derivative expression:

f'(π/2) = -sin(π/2) - π/3*cos(π/3)(π/2)

Since sin(π/2) = 1 and cos(π/3)(π/2) = cos(π/3), we can simplify further:

f'(π/2) = -1 - π/3*cos(π/3)

The value of the derivative of the function f(x) at x0 = π/2 is -1 - π/3*cos(π/3).