Directional derivative is maximum when  
the direction is along the gradient 

Change parameters uisng slider, compare values of dierectional 
derivative and gradient as you move through different angles.
Correlate  2D and 3D graphics

ds = 0.14 (slider from 0 to 0.5, step 0.01)
θ = 0.3490658503988659 rad (slider from 0 to 6.283185307179586, step 0.08726646259971647)
Y_1 = -0.7451418360509362 (slider from -20 to 20, step 0.01)
X_1 = 0.6511917477206637 (slider from -10 to 10, step 0.01)
f(x, y) = (-x^(2)) - y^(2)
H: (X_1 + (ds * cos(θ)), Y_1 + (ds * sin(θ)), f(X_1 + (ds * cos(θ)), Y_1 + (ds * sin(θ))))
B: (X_1, Y_1, f(X_1, Y_1))
a_1 = Plane(B, xOyPlane)
t = Segment(B, H)
k = Derivative(f, y, 1)
a = Derivative(f, x, 1)
v = Vector((X_1, Y_1, f(X_1, Y_1)), (X_1 + a(X_1, Y_1), Y_1 + k(X_1, Y_1), f(X_1, Y_1)))
w = Vector(B, H)
u = Vector((X_1, Y_1), (X_1 + cos(θ), Y_1 + sin(θ)))
A: (X_1, Y_1)
e = Vector((X_1, Y_1, f(X_1, Y_1)), (X_1 + cos(θ), Y_1 + sin(θ), f(X_1, Y_1)))
text4: "unit vector in the required direction=" + u + ""
g = Vector((X_1, Y_1), (X_1 + a(X_1, Y_1) / sqrt(a(X_1, Y_1)^(2) + k(X_1, Y_1)^(2)), Y_1 + k(X_1, Y_1) / sqrt(a(X_1, Y_1)^(2) + k(X_1, Y_1)^(2))))
text5: "unit gradient vector=" + g + ""
gradf = Vector((X_1, Y_1), (X_1 + a(X_1, Y_1), Y_1 + k(X_1, Y_1)))
j = Vector((X_1, Y_1, f(X_1, Y_1)), (X_1 + a(X_1, Y_1) / sqrt(a(X_1, Y_1)^(2) + k(X_1, Y_1)^(2)), Y_1 + k(X_1, Y_1) / sqrt(a(X_1, Y_1)^(2) + k(X_1, Y_1)^(2)), f(X_1, Y_1)))
X = Textfield(X_1)
Y = Textfield(Y_1)
D: (X_1 + (ds * cos(θ)), Y_1 + (ds * sin(θ)), f(X_1 + (ds * cos(θ)), Y_1 + (ds * sin(θ))))
i = Segment(B, A)
C: (X_1 + (ds * cos(θ)), Y_1 + (ds * sin(θ)))
l = Segment(C, D)
m = Segment(A, C)
E: (1, 1.5)
F: (1, 1.5, 3.25)
p = Segment(E, F)
G: (X_1 + (ds * cos(θ)), Y_1 + (ds * sin(θ)))
q = Segment(H, G)
r = Segment(A, E)
s = Segment(B, D)
f_1 = OrthogonalLine(B, v, xOyPlane)
n: (a(X_1, Y_1) * cos(θ)) + (k(X_1, Y_1) * sin(θ))
magnitudegradf = Length(gradf)
L = Sequence(f(x, y) = a, a, -4, 0)
text7: "Magnitude of the Gradient =" + magnitudegradf + ""
text1: "Directional derivative (along u) =" + n + ""