Gradient Calculator
Calculate the gradient vector (nabla f) of a scalar function in 3D space.
Scalar Function f(x, y, z)
Use: x, y, z, ^, sin, cos, tan, exp, log, sqrt, pi
Point of Evaluation
Numerical Settings
Gradient Formula
nabla f = (df/dx, df/dy, df/dz)
Gradient Vector nabla f
(2.0000, 4.0000, 6.0000)
at point (1, 2, 3)
ff(x,y,z)
14.000000
|nabla||nabla f|
7.483315
dxdf/dx
2.000000
dydf/dy
4.000000
Unit Direction (Steepest Ascent)
(0.2673, 0.5345, 0.8018)
Gradient Properties
- Points in direction of steepest increase
- Magnitude = maximum rate of change
- Perpendicular to level surfaces
- Used in optimization algorithms
About the Gradient
Definition
The gradient of a scalar function is a vector field that points in the direction of the greatest rate of increase of the function. Its magnitude represents the rate of increase in that direction.
Applications
- Machine learning optimization
- Finding extrema of functions
- Heat flow and diffusion
- Electric and gravitational fields