Question

Find the gradient of the function and the maximum value of the directional derivative at the given point.

h(x,y)=ycos(x-y) (0,pi/3)

Answer 1

I want to see if I've done this right. So taking the partial derivative, I get

\[\Delta h(x,y)=-ysin(x-y)i+\cos(x-y)+ysin(x-y)\]

Answer 2

and then evaluating at (0,pi/3) would get me:\[ (-\pi/3)(-\sqrt{3}/2)+(-\sqrt{3}/2)+(\pi/3)(-\sqrt{3}/2)\]

Answer 3

Gradient meaning U've got to fing dy/dx is it????????

Answer 4

Yeah, you have to take the partial derivative of each term: \[\Delta f(x,y)=f_{x}(x,y)i+f _{y}(x+y)j\]

Answer 5

gfradient is (fx (x,y),fy(x+y))
is a vector.
If they asking you for maximum value, i would say they asking either for modul or just the value of partial derivatives at the point