ch14sec3 - 14.3 Partial Derivatives For a one variable...

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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 ( ) f x 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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