to
let people know that we are holding Calculus
Lesson
64
Partial
Derivatives
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Back to Dr. Nandor's Calculus Page
For a function of more than one variable, we may want to know
what happens if we vary just one of them. The procedure
is basically the same as what we already know, except
that we use the to
let people know that we are holding
everything constant except for 
(in
this example).
Example: 
Now, what if we want to know how 
varies
with respect to 
regardless of how the other variables change? Then we use
the chain rule. Note here that we use the notation 
instead
in the chain rule since
it may be that 
. If we only
have 
then 
, which is why we have only
seen
up to this point in our
studies. So,
Examples: 
For each, what is each partial derivative? What is the
derivative wrt 
?
Redo each of the above examples if 
without rewriting
the function.