📐 Multivariable Calculus Visualizer

Visualise 3D surfaces, compute partial derivatives, explore tangent planes and gradients – all interactively.

🧮 Function f(x,y)

📍 Point (x₀, y₀)

x₀ 0.0 y₀ 0.0

f(x₀,y₀)—

∂f/∂x—

∂f/∂y—

Gradient magnitude—

📖 Tangent Plane

                            z = f(x₀,y₀) + fₓ(x−x₀) + fᵧ(y−y₀)
                        

Show tangent plane

💡 How it works

Surface: 3D plot of f(x,y)
Point: red sphere at (x₀,y₀,f(x₀,y₀))
Tangent plane: linear approximation at that point
Gradient: vector of partial derivatives, points uphill

📖 Key Concepts

Partial derivatives measure the rate of change of f with respect to x (keeping y constant) and y (keeping x constant).
The gradient ∇f = (fₓ, fᵧ) points in the direction of steepest ascent; its magnitude is the slope in that direction.
The tangent plane is the best linear approximation to the surface near a point – it's the multivariable analogue of a tangent line.