My function is: Z = f(x,y) = ln(x^2+y^2+1)
and I am finding the directional derivatives,
grad Z.u, grad Z.v, from point A(3,3,3.56) to
points B(1,-2,1.79) and C(-3,3,2.94).
For AB = -2i-7j, the unit vector in the direction of AB is:
u = -2i/(53^.5)-7j/(53^.5)
and AC = -6i-2j , the unit vector in the direction of AC is:
v = 6i/(40^.5)- 2j/(40^.5)
Grad Z = (2x/(x^2+y^2+1))i+(2y/(x^2+y^2+1))j
and then
Grad Z at(3,3)=(6/35)i+(10/35)j
grad Z.u = [6/35)i+(10/35)j].[(-2/(53^.5))i-(7/(53^.5))j]
= 0.2276260774
grad Z.v = [(6/35)i+(10/35)j].[(6/(40^.5))i+(-2/40^.5)j]
= 5.443635115
