Suppose a function f (t) = 0(adsbygoogle = window.adsbygoogle || []).push({});

x (t) -y (t) = 0

with

x = t

y = t

df/dt = 0

However

∂f/∂x = 1

This case may seem obvious to most of the regulars this forum, but took me by surprise when I was reading a math book that I needed to "derive from both sides" (I assumed that as a side was zero, or other would always be).

I wonder if there is any book that deals with these things in a more elegant way. To respond in a clear way, when I can "derive from both sides."

Because for example:

x (t) - y (t) = 0

"deriving from both sides":

∂x/∂x - ∂y/∂x = 0

1 = 0

Many thanks for the help, and sorry if my question is very simple.

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# If f = 0, then df/dt=0, but ∂f/∂x≠0

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