Let f(x, y, z)=yz+xz-6. At the point x=1, y=1, z=1, find the unit vector that points in the direction for which f is increasing at the fastest rate.
Let F(x, y) be the vector field ((x-y)/(x^2+y^2), (x+y)/(x^2+y^2)). Compute curl(F).
Find a potential function for the vector field f(x, y)=2x/y i+(1-x^2)/y^2 j.
Find the principal unit normal vector to the curve defined by r(t)=<t, t^2>. T(t)=1/sqrt(1+4t^2)i+2t/sqrt(1+4t^2)j I need to find T'(t) using quotient rule but don't know...