Concept: The value of a partial derivative depends on the value(s) of what is held constant (editing)

Prerequisite concepts

Derivatives can be found while holding one or more variables constant

Derivatives of multivariable functions can be found by holding one or more variables constant (subject to physical limitations).

There is a partial derivative in every direction at any point

The value of a partial derivative depends on the value(s) of what is held constant

FIXME: Is this really a statement about paths? I don't think we have path-related concepts.

Representations used

NEEDS NAME

$\left(\frac{\partial f}{\partial x}\right)_y$

ENTER LONG DESCRIPTION

Partial Derivative Machine Derivatives

Partial derivatives that do not have the same variable(s) held constant (at the same values?) are not the same derivative

FIXME

There are experimental limits to how $small$ of a change can be measured The derivative can be interpreted physically The coefficients in a differentials equation are partial derivatives

There is a partial derivative in every direction at any point There is a tangent line in every direction at every point The value of a partial derivative depends on the value(s) of what is held constant The magnitude of the gradient is proportional to the density of contour lines

The magnitude of the gradient is proportional to the density of contour lines The direction of the gradient is perpendicular to contour lines The gradient is a local quantity The gradient lives in the domain and has the same number of spatial dimensions as the original function