My Math Forum Chain rule and second order derivatives
 User Name Remember Me? Password

 Calculus Calculus Math Forum

 September 1st, 2016, 05:05 AM #1 Member   Joined: Mar 2015 From: uk Posts: 33 Thanks: 1 Chain rule and second order derivatives I'm trying to work out the following question:- Use the chain rule to show that (d2y/dx2).((dx/dy)^3) + d2x/dy2 = 0 I picked y=x^3 to convince myself that it is correct (for that equation) but don't know how to go about using the chain rule to prove it There is a hint saying: (dy/dx).(dx/dy) = 1 differentiate this Thanks
 September 1st, 2016, 05:14 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2604 Math Focus: Mainly analysis and algebra What happens if you write $v(y)={\mathrm d x \mathrm d y}$, giving $y'v=1$? Differentiate implicitly. Thanks from topsquark and wirewolf
 September 1st, 2016, 04:15 PM #3 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 dy/dx=y' dx/dy=1/y' d$\displaystyle ^{2}$x/dy$\displaystyle ^{2}$=-(1/y'$\displaystyle ^{2}$)y''(dx/dy)=-(1/y'$\displaystyle ^{3}$)y'' Substituting into OP: y''(1/y'$\displaystyle ^{3}$)-(1/y'$\displaystyle ^{3}$)y''=0 Thanks from topsquark
September 2nd, 2016, 05:45 AM   #4
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 124

Quote:
 Originally Posted by v8archie What happens if you write $v(y)={\mathrm d x \mathrm d y}$, giving $y'v=1$? Differentiate implicitly.
Nothing happens. A function can't equal a product of differentials.

 September 10th, 2016, 03:13 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2604 Math Focus: Mainly analysis and algebra Yes. There was quite obviously a typo in that post. Luckily the OP was able to see that, even if you were not.
 September 10th, 2016, 06:50 PM #6 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 There was no indication anyone understood what you meant until after I responded.
 September 10th, 2016, 07:47 PM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2604 Math Focus: Mainly analysis and algebra You mean apart from the people who thanked me.
September 10th, 2016, 08:09 PM   #8
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 124

Quote:
 Originally Posted by wirewolf There is a hint saying: (dy/dx).(dx/dy) = 1 differentiate this
OP thanked you after my post. If they understood what you meant, why would they thank you for repeating the hint in OP?

 Tags chain, derivatives, order, rule

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post green21317 Calculus 1 February 3rd, 2014 03:05 AM praneeth101 Calculus 5 December 15th, 2012 12:30 PM lilwayne Calculus 2 October 1st, 2010 06:36 PM mezzeric Calculus 1 February 22nd, 2010 02:27 PM Brutulf Calculus 2 May 29th, 2009 04:49 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top