lanedance said:wouldn't it need fx(2,1) = fy(2,1) = 0 as well?
A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables, while holding all other variables constant.
A regular derivative measures the rate of change of a function with respect to one variable, while a partial derivative measures the rate of change of a function with respect to one variable while holding all other variables constant.
A statement about a partial derivative can be true or false depending on whether the rate of change of the function in question is correctly described by the statement.
Yes, a partial derivative can be negative if the rate of change of the function is decreasing in the direction of the variable being considered.
Partial derivatives are used in many fields of science and engineering to analyze and model systems that involve multiple variables changing simultaneously. Examples include economics, physics, and engineering.