Differential Calculus2D
Partial Differentiation - Theory & Concepts - Gradient Vector
Expand calculus to multivariable functions, partial derivatives, the gradient vector, the second partials test, and Lagrange Multipliers.
Open the complete lessonGradient Vector Visualization
Surface: f(x, y) = x² + y²
Current State
Position (x, y)(0.00, 0.00)
∇f = <2x, 2y><0.00, 0.00>
Magnitude |∇f|0.00
Move your mouse over the grid. Notice how the red gradient vector always points directly outward from the origin, perpendicular to the circular level curves. This shows the direction of steepest ascent on the paraboloid surface.