Partial derivative second order

  • #1
402
14

Homework Statement


Hi guys, I am have a problem with the question displayed below:

upload_2017-2-15_23-33-6.png
[/B]

Its 6.1 ii) I am really not sure how I am suppose to approach this. I am new to partials, so any advice would be great.

Homework Equations




The Attempt at a Solution


So far I have:
$$\frac{\partial ^2 f}{\partial x^2}=\frac{\partial}{\partial x}\frac{\partial f}{\partial x}=\frac{\partial}{\partial x}\frac{-x}{r^3} $$

using quotient rule:

$$=[\frac{\partial}{\partial x}(-x)(r^3)-(-x)(\frac{\partial}{\partial x}r^3)]/r^6$$

$$\frac{\partial}{\partial x}r^3=3r^2\frac{\partial r}{\partial x}=3r^2*(x/r)=3rx$$

subbing the above into the quotient and simplifying
I get
$$\frac{-r^2+3x^2}{r^5}$$

[/B]
 

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
2019 Award
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using quotient rule:
might not be the best thing to do. How did you find ##\partial f\over\partial x## ?
And: was 6 i) allright and clear ? How come 6 ii) is then problematic ?

[edit] Stupid me o:) . Your working is completely correct. Well done...
'Quotient rule' confused me, but it works just fine. My approach would be to use the chain rule -- with, of course, the same result. Matter of preference, not matter of 'best thing to do'.
 
Last edited:
  • #3
Ray Vickson
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Homework Statement


Hi guys, I am have a problem with the question displayed below:

View attachment 113277[/B]

Its 6.1 ii) I am really not sure how I am suppose to approach this. I am new to partials, so any advice would be great.

Homework Equations




The Attempt at a Solution


So far I have:
$$\frac{\partial ^2 f}{\partial x^2}=\frac{\partial}{\partial x}\frac{\partial f}{\partial x}=\frac{\partial}{\partial x}\frac{-x}{r^3} $$

using quotient rule:

$$=[\frac{\partial}{\partial x}(-x)(r^3)-(-x)(\frac{\partial}{\partial x}r^3)]/r^6$$

$$\frac{\partial}{\partial x}r^3=3r^2\frac{\partial r}{\partial x}=3r^2*(x/r)=3rx$$

subbing the above into the quotient and simplifying
I get
$$\frac{-r^2+3x^2}{r^5}$$
[/B]
Your answer is correct. It is a matter of taste whether you leave your final numerator as ##3x^2-r^2##, or re-write it as ##2x^2-y^2-z^2##.

BTW: Remove all those offensive bold fonts: it looks like you are yelling at us.
 
  • #4
402
14
thank for the responses. I will remove bold next, i did not even notice it was bold.
 

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