Prerequisite concepts
INSERT URL HERE
lower anchor MTH 254
Concepts taught
The derivative is a local quantity
Partial derivatives are functions
The gradient is a function
The value of the derivative does not depend on what is happening far away from the point at which the derivative is being evaluated: it can be determined by what is happening in the neighborhood of the point. Geometrically, the derivative (slope) of a curve at a point is not a statement about the general shape of the curve but rather about the behavior of the curve immediately around that point.
The partial derivative of a function is itself a function (although taking a partial derivative at a point will just give a number). This means that the value of the partial derivative at different points in the domain will, in general, be different.
The gradient of a function (unless taken at a single point) is itself a function