Partial Derivatives


Consider   z=f(x,y) 

If we differentiate  w.r.t.  x   considering   y   as constant , we get the partial derivatives as


= dz/dx  or  fx  

Similarly keeping  constant we can differentiate  w.r.t.  y  we get ;


=dz/dy   or  f 

If we differentiate   df/dx   again w.r.t.   x  keeping    y   as constant  

we get the second order partial derivatives 


If we differentiate   df/dx  w.r.t.   y ,  keeping    x  as constant ,

we get another second order partial derivatives


Similarly two more derivatives


and (d/dy)(df/dy) .


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