Partial Derivatives of Functions of More than one independent variable                                          

 

 

In a Nut Shell:  Recall the derivative of a function of one independent variable (say x)

relates directly to the slope of the dependent variable (say y).  i.e. dy/dx

 

 

In a Nut Shell:  Likewise for function   z   of two independent variables ( say  x  and  y  ),

the partial derivative on  x  gives the slope in the  x-direction and the partial derivative on

 y  gives the slope  in the y direction.    i.e.  ∂z/∂x  and  ∂z/∂y     This notion of partial

 derivatives holds for functions of any number of independent variables.

 

 

 

 

 

Start by reviewing the definition of the derivative for a function of one independent

variable, x

 

                  df/dx  =    f ’(x)  =   lim [ f(x + h)  -   f(x)]/ h

                                                h → 0

               

 

With one independent variable,  f ’(x) represents the slope of the curve  f(x) at point P.

 

 

 

Click here to continue with discussion of partial derivatives.

 



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