- #1

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[tex]\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][/tex]

holds true for all

*f(x,y).*Thanks.

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- Thread starter 2sin54
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- #1

- 109

- 1

[tex]\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][/tex]

holds true for all

- #2

jedishrfu

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http://www.math.ucsd.edu/~mradclif/...ureNotes/second_order_partial_derivatives.pdf

Are you trying to prove this?

- #3

- 109

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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.

http://www.math.ucsd.edu/~mradclif/...ureNotes/second_order_partial_derivatives.pdf

Are you trying to prove this?

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