Mastering Functions of Two Variables

Partial derivatives are used to find the integral of a function with respect to one variable while keeping the other variables constant.

Partial derivatives are used to find the slope of a function with respect to all variables simultaneously.

Partial derivatives are used to find the slope of a function with respect to one variable while keeping the other variables constant. (correct)

Partial derivatives are used to find the integral of a function with respect to all variables simultaneously.

The gradient vector represents the average rate of change of a function.

The gradient vector represents the direction of steepest ascent of a function. (correct)

The gradient vector represents the direction of steepest descent of a function.

The gradient vector represents the instantaneous rate of change of a function.

The Chain Rule allows us to find the derivative of a composition of functions. (correct)

The Chain Rule allows us to find the slope of a function with respect to one variable while keeping the other variables constant.

The Chain Rule allows us to find the integral of a composition of functions.

The Chain Rule allows us to find the slope of a function with respect to all variables simultaneously.