Verified answer

a = 1/x

x * cos(1/x) =>

cos(1/x) / (1/x) =>

cos(a) / a

u = cos(a)

u' = -sin(a) * a'

v = a

v' = a'

(v * u' - u * v') / v^2 =>

(a * (-sin(a) * a') - cos(a) * a') / a^2 =>

-(a * sin(a) + cos(a)) * a' / a^2

a = 1/x

a' = -1/x^2

-((1/x) * sin(1/x) + cos(1/x)) * (-1/x^2) / (1/x)^2 =>

(1/x) * sin(1/x) + cos(1/x)

x = 2/pi

1/x = pi/2

(pi/2) * sin(pi/2) + cos(pi/2)

y = u * v

dy/dx = v* du/dx + u* dv/dx

f'(x) =( 1)(cos 1/x) + (-1/x^2) (-sin 1/x) (x) =

cos (1/x) + (1/x) sin (1/x)

f'( 2/π) = cos π/2 + (π/2) sin π/2 =

f' (2/π) = π/2 ◄◄◄ the answer

First, evaluate the derivative of f(x) & write the answer here.

Then we will take it from there.