Expert: Paul Klarreich - 10/7/2009

Question
hi,
I need help in finding the proof of second derivative
that is
(d^2)y/d(x^2)=(dy'/dt)/(dx/dt)
if x=f(t) and y=g(t)

Thank you.

Answer
Questioner: Amelia
Country: United States
Category: Calculus
Private: No
Subject: find the proof of second derivative
Question: hi,
I need help in finding the proof of second derivative
that is
(d^2)y/d(x^2)=(dy'/dt)/(dx/dt)
if x=f(t) and y=g(t)

Thank you.
....................................
Hi, Amelia,
.........................................
WARNING: THIS DISCUSSION MAY CONTAIN FRACTIONS AND OTHER MATERIAL DIFFICULT TO VIEW ON CERTAIN COMPUTING SYSTEMS.  VIEW IT IN A FIXED-SIZE FONT, SUCH AS COURIER.
.........................................

Start with:
(d^2)y/d(x^2)   << Actually, you mean to write:  (d^2)y/(dx)^2

d  dy
-- -- =
dx dx

d  dt dy
-- -- -- =  << insert  dt/dt
dx dt dx

d  dy dt
-- -- -- =  << rearrange a bit.
dx dt dx

d  dy   dx
-- -- / -- =   << invert
dx dt   dt

d  dy   dx
-- -- / -- = << rearrange a bit.
dt dx   dt

d        dx
--(y') / -- =
dt       dt

I think that's it.