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Partial Derivatives Visualizer
Calculus III · Multivariable Calculus
Learning Objectives
Visualize f(x,y) as a 3D surface
∂f/∂x: slope holding y constant
∂f/∂y: slope holding x constant
Gradient vector ∇f points uphill
Definitions
∂f/∂x
= lim_{h→0} [f(x+h,y) − f(x,y)] / h
∂f/∂y
= lim_{h→0} [f(x,y+h) − f(x,y)] / h
∇f
= ⟨∂f/∂x, ∂f/∂y⟩ (Gradient)
Tags
partial derivatives
gradient
multivariable
3D surface
SURFACE f(x,y)
Paraboloid: x² + y²
Saddle: x² − y²
Wavy: sin(x)·cos(y)
Gaussian: e^(−x²−y²)
Point x₀
0.00
Point y₀
0.00
f(x₀, y₀)
—
∇f magnitude
—
∂f/∂x
—
∂f/∂y
—
Red line
: tangent in x-direction (∂f/∂x)
Green line
: tangent in y-direction (∂f/∂y)
Yellow dot
: evaluation point (x₀, y₀)
Drag to rotate the 3D surface.