I'm new at working with directional derivatives. I'm stuck on this problem. Would someone mind helping me with the "Point" and "Direction" parts of the problem. I'm just looking for a place to start, not for someone to do the problem for me. Thanks.
In each of the following, find the directional derivative of f at P in the given direction.
1. f(x,y)=xy(1-x^2-y^2), P=any point on the unit circle, Direction: in the direction of OP.
I found that the gradient of f is: <y(1-x^2-y^2)-2yx^2, x(1-x^2-y^2)-2xy^2>, so I'm stuck on finding P and the direction.
Ok, I did the problem, would you mind checking for me? Thanks
So I changed [the format] of f (x,y) = (xy-x^3y-xy^3)
and P=(a,b) & OP=<a,b>
Now I have the gradient of f=<y-3x^2y-y^3, x-x^3-3xy^2>
Duf(x,y)=(a)(y-3x^2y-y^3)+(b)(x-x^3-3xy^2)
Duf(a,b)=(a)(b-3a^2b-b^3)+(b)(a-a^3-3ab^2)
Duf(a,b)= (ab-3a^3b-ab^3) + (ab-a^3b-3ab^3)
Duf(a,b)= 2ab-4a^3b-4ab^3
Duf(a,b)= ab-2a^3b-2ab^3
Duf(a,b)= ab(1-2a^2-2b^2)