a simple Cross-derivative question

From: Ekaterina (raskurnikov_at_yahoo.es)
Date: 09/19/04 

Date: Sun, 19 Sep 2004 15:51:37 +0000 (UTC)

Define a function as follows,

f(x,t):R^2----->R

is it true that if

df(x,t)
------- = 0 when t=0
dt

then

df(x,t)
------- = 0 when t=0 ???
dtdx