No, not exactly. My f(x,y) is a huge compound function and it's a hassle to differentiate with respect to both variables and then take the limit, as opposed to differentiating by x, setting the limit and then differentiating (the now simpler function) by y.jedishrfu said:I think this is true provided the mixed partial derivatives of function f(x,y) are continuous at x=0 and whatever y=value.
http://www.math.ucsd.edu/~mradclif/teaching/Math10C/LectureNotes/second_order_partial_derivatives.pdf
Are you trying to prove this?
A limit operator is a mathematical operator that represents the limit of a function as its input values approach a certain value or point. It is denoted by the symbol "lim" and is commonly used in calculus.
A differential operator is a mathematical operator that represents the derivative of a function. It is denoted by symbols such as "d/dx" or "∂/∂x" and is also commonly used in calculus.
Two operators commute if their order of operation does not affect the final result. In other words, if the two operators can be interchanged without changing the outcome, then they are said to commute.
No, limit and differential operators do not always commute. The order of operation can affect the final result, especially when considering more complex functions.
To determine if two operators commute, you can try interchanging their order of operation and see if the result changes. If the result remains the same, then the operators commute. However, this may not be applicable for all cases, especially for more complex functions.