Calculus
Advanced

Gradient Vector

Vector of partial derivatives pointing in the steepest ascent.

Formula

∇f=(∂f∂x,∂f∂y)\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right)

Variables

fScalar field

Example

Points uphill on a surface

Did You Know?

The gradient always points in the direction of steepest ascent, which is why "gradient descent" trains AI models.

multivariable