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Chap14sec3 - 14.3PartialDerivatives , of...

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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  ( ) f x , then  df dx  is  the slope, or rate of change, of the graph of  f 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.  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 
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