Partial Derivative Calculator

Calculate partial derivatives of multivariable functions numerically.

Function

f(x, y, z) =

Use: x, y, z, +, -, *, /, ^, sin, cos, tan, log, exp, sqrt

Quick Examples

Point of Evaluation

x =

y =

z =

Function Value

f(2, 3, 1) =

13.000000

First Partial Derivatives

df/dx

4.0000

df/dy

6.0000

df/dz

0.0000

Gradient Vector

grad f = (4.000, 6.000, 0.000)

|grad f| = 7.2111

Second Partial Derivatives

d^2f/dx^22.0000

d^2f/dy^22.0000

d^2f/dxdy (mixed)0.0000

Laplacian

nabla^2 f = d^2f/dx^2 + d^2f/dy^2

4.0000

Partial Derivative Concepts

Partial Derivative

df/dx = lim(h-0) [f(x+h,y) - f(x,y)] / h

Derivative with respect to one variable, treating others as constants.

Gradient

grad f = (df/dx, df/dy, df/dz)

Vector pointing in direction of steepest increase.