Function Selection
Choose from preset mathematical functions to visualize
3D Surface Visualization
Point Position Controls
View Controls
Color Legend
Surface z = f(x,y)
∂f/∂x curve (y constant)
∂f/∂y curve (x constant)
Point (x₀, y₀, f(x₀,y₀))
Partial Derivatives at Current Point
∂f/∂x (keep y constant):
∂f/∂x = cos(x)·cos(y)
Red curve on surface shows: slope = 0.00
The red curve is the intersection of the surface with the plane y = y₀
∂f/∂x = cos(x)·cos(y)
Red curve on surface shows: slope = 0.00
The red curve is the intersection of the surface with the plane y = y₀
∂f/∂y (keep x constant):
∂f/∂y = -sin(x)·sin(y)
Green curve on surface shows: slope = 0.00
The green curve is the intersection of the surface with the plane x = x₀
∂f/∂y = -sin(x)·sin(y)
Green curve on surface shows: slope = 0.00
The green curve is the intersection of the surface with the plane x = x₀
Key Concept: The colored curves lie on the surface. Each partial derivative measures the slope of the curve you get when you slice the surface with a vertical plane. The semi-transparent planes show where we're cutting the surface. The arrows show the direction and magnitude of the slope at the yellow point.
Mouse Controls: Click and drag to rotate, Scroll to zoom, Right-click drag to pan