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14.3 Partial Derivatives
For a one variable function, it is easy to interpret what is meant by
rate of change
.
If the
function is
, then
()
fx
df
dx
is the slope, or rate of change, of the graph of
at a point. There
is a problem with this interpretation when we speak of functions of more than one variable.
Derivative
still means
rate of change
but now we can speak of a rate of change
with respect to
several different variables.
f
A function of more than one variable may have derivatives with respect to each independent
variable. These derivatives in turn may have derivatives with respect to each independent
variable. Such derivatives are called
partial derivatives
. Partial derivatives are simply ordinary
derivatives with respect to one variable while keeping the other variable constant. Partial
derivatives can be found by using our previously obtained differentiation formulas. We call
these partial derivatives because we are only differentiating the function in one direction.
Thus, we only get a partial picture of how this function changes as the variables change. The
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 Fall '08
 Estrada
 Derivative, Rate Of Change, Slope

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