It would be the second option. It is not asking you to find the rate of change in the direction of , it is asking for the rate of change of the function along the parametrized curve. You would need to use the differential method.
Ok so I'm having a little trouble figuring out which method I am supposed to use to solve this problem.
Calculate the derivative of f(x,y)= (y-x^2)/3y along the curve parameterized by r(t)= 2t(i) - t^(1/2)(j) when t=4.
Do I put the 4 in for t and then use that as the direction and find the directional derivative, or is this a chain rule problem where I take
df/dx * dx/dt + df/dy * dy/dt? Any help would be greatly appreciated. Thanks.
Ok. so I made it through using this method, and I'm thinking that I should be able to set x=2t and y= -t^(1/2) insert the t=4 and solve, then insert these into my final differential giving me a scalar answer since the original function is parameterized by r(t)= 2t(i) - t^(1/2)(j). Is this correct?