Gradient

The gradient of a function is a collection of all its partial derivatives.

For a function , the gradient is denoted by . The symbol is called "nabla" or "del", although "del" refers more to the operator instead of the actual symbol. The formula for the gradient is:

Alternatively, the gradient can be written as a summation:

Where is the th unit vector (, , etc.).

The gradient is a vector that points in the direction of the greatest increase of the function.

Properties

The gradient can be thought of as the multivariable analog of the derivative. Therefore it has similar properties to the derivative.

Linearity

The gradient is a linear operator. This means that for any two functions and and any scalar , the following holds: