Define a surface, choose a point (including expressions like pi/2), select a unit direction, and see the directional derivative.
Examples: x^2+y^2, x^2-y^2, sin(x)+cos(y), x*y, 3*exp(x)*sin(y)
e.g. 0, pi/2, sqrt(2)
e.g. pi/2, -pi, 1/3
3D surface
P = (x₀, y₀, f(x₀, y₀)). The blue arrow shows the selected directional change on the tangent plane.
Choose a direction u
Each radius is a unit vector in the xy-plane. Click a direction.
Directional derivative at P
P =
∇f(P) =
u =
Duf(P) = ∇f(P) · u
∇f(P) =
u =
Duf(P) = ∇f(P) · u
0
Positive means the surface rises in that direction; negative means it falls; zero means no first-order change.