derivative

• Oct 30th 2009, 06:51 PM
mahefo
derivative
Help me explain the formula:
"for $f(t,\widetilde{Z}(t))$ we have:
$df=\frac{df}{dt}[dt]+\frac{df}{dz}[dZ]+\frac{1}{2}\frac{d^2 z}{dz^2}[dt]$
$\frac{df}{dt},\frac{df}{dz},\frac{d^2f}{dz^2}$ are usual derivatives from calculus."
Thanks a lot.
• Oct 31st 2009, 01:04 AM
HallsofIvy
Quote:

Originally Posted by mahefo
Help me explain the formula:
"for $f(t,\widetilde{Z}(t))$ we have:
$df=\frac{df}{dt}[dt]+\frac{df}{dz}[dZ]+\frac{1}{2}\frac{d^2 z}{dz^2}[dt]$
$\frac{df}{dt},\frac{df}{dz},\frac{d^2f}{dz^2}$ are usual derivatives from calculus."
Thanks a lot.

Well, I can't explain it. For one thing, I have no idea what $\frac{d^2 z}{dz^2}$ could mean, if it isn't 0!
$\frac{dz}{dz}= 1$ so differentiating again gives 0.