# I Do limit and differential operators commute?

1. Feb 16, 2017

### 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.

2. Feb 16, 2017

### Staff: Mentor

3. Feb 16, 2017

### 2sin54

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.