Im not sure how to do this Any help is appreciated Suppose f

I\'m not sure how to do this. Any help is appreciated.

Suppose f(x, y) = sin(2y/x) and u is the unit vector in the direction of. Then, f(x, y) = f(2, pi) = fu(2, pi) = Duf(2, pi) =

Solution

a)

grad(f) = (df/dx , df/dy) = (-2y/x^2 cos(2y/x) , 2/x cos(2y/x) )

b)

grad(f(2,)) = (-/2 cos() , cos()) = (/2 , -1)

c)

Du = grad(f).u/|u| = (/2 , -1).(2,)/(4+^2) = (-)/(4+^2) = 0/(4+^2) = 0