# Do limit and differential operators commute?

• I
2sin54
In general I'm wondering if

$$\lim_{x\to0} \left[\frac{d}{dy} \frac{d}{dx} f(x,y)\right] = \frac{d}{dy} \left[\lim_{x\to0} \frac{d}{dx} f(x,y)\right]$$

holds true for all f(x,y). Thanks.

## Answers and Replies

Mentor
I think this is true provided the mixed partial derivatives of function f(x,y) are continuous at x=0 and whatever y=value.