For functions that depend on two or more variables, the partial differential represents the change in the function with one of the variables as the other variables are held constant. The ordinary differential for such functions represents the total change as a result of differential changes in all variables.

a. True
b. False

Truly, for a multivariable function, that is, one which depends on two or more variables, the partial differential represents the change in the function with one of the variables as the other variables are held constant.

For example, a function z which has x and y as its independent variables

z = f(x, y)

The function has partial derivatives (∂f/∂x) (which is the derivative of the function with respect to x, holding y constant) and (∂f/∂y) (the derivative of the function with respect to y, holding x constant).

But to obtain the differential changes in all the variables, a differential known as the total differential is used.

The total differential, for our example function z, is given as

dz = (∂f/∂x) dx + (∂f/∂y) dy

This isn't called the ordinary differential.

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