Question about Second Order Partial Derivatives | Mathematics | Page 1

distant sluice Oct 31, 2024, 2:47 PM

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patent pivotBOT Oct 31, 2024, 2:48 PM

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distant sluice

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distant sluice Oct 31, 2024, 2:48 PM

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for this question what second order derivatives would I need

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i have u_x, u_y, u_z and then the second order u_xx, u_yy, u_zz so far

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do I need to do all combinations for it

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like u_xy, u_xz, u_zy?

queen cairn Oct 31, 2024, 2:54 PM

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distant sluice i have u_x, u_y, u_z and then the second order u_xx, u_yy, u_zz so far

So here, you can see it as a tree that you need to complete.
0-th order: u
1st order: u_x, u_y, u_z
2nd order: u_xx, u_xy, y_xz, u_yx, u_yy, u_yz, u_zx, u_zy, u_zz

distant sluice Oct 31, 2024, 2:54 PM

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😭

queen cairn Oct 31, 2024, 2:54 PM

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Do note however that in the second order, many of them are identical

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I forgot the name of the theorem

distant sluice Oct 31, 2024, 2:54 PM

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yeah thats what I was thinking

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I went over that in class so I thought they'd be the same

queen cairn Oct 31, 2024, 2:54 PM

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So in practice, for the second order, you can reduce it from 9 to like, 6

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since for instance u_xy = u_yx

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it's a bit tedious, you can't avoid that

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on the bright side the function is relatively simple to differentiate

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So grit your teeth for 2 minutes and you'll be done

distant sluice Oct 31, 2024, 2:56 PM

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yeah the x and z ones differentiate the same just different letters

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in my test last week I forgot that differentiating (ln(x))' = (x)'/x

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so I just had it written as say (ln(5x))' = 1/5x

queen cairn Oct 31, 2024, 3:00 PM

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distant sluice so I just had it written as say (ln(5x))' = 1/5x

well, you're missing points on writing the equal sign

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because ln(5x) is definitely not equal to 1/5x

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and secondly, seeing that ln(5x) = ln(5) + ln(x), this is quite simple to differentiate

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3am

distant sluice Oct 31, 2024, 3:01 PM

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it was some double chain rule equation :(

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with sin inside so it fried my brain a bit

queen cairn Oct 31, 2024, 3:01 PM

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yes, but calculus is better when you don't have to calculate

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no_pain

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Anyway, do you still need help for this problem?

distant sluice Oct 31, 2024, 3:03 PM

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no i think I got it

honest gyro Oct 31, 2024, 3:03 PM

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queen cairn I forgot the name of the theorem

Schwartz theorem

distant sluice Oct 31, 2024, 3:04 PM

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thank you guys

queen cairn Oct 31, 2024, 3:04 PM

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Dankeschön

distant sluice Oct 31, 2024, 3:04 PM

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i forgor how to rep

queen cairn Oct 31, 2024, 3:04 PM

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distant sluice thank you guys

In that case, please close the post

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by concatenating a plus sign with "close"

distant sluice Oct 31, 2024, 3:05 PM

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+close

tired harborBOT Oct 31, 2024, 3:05 PM

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distant sluice +close

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tired harborBOT Oct 31, 2024, 3:05 PM

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tired harbor

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#Question about Second Order Partial Derivatives