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October 20th, 2009, 01:56 PM  #1 
Member Joined: Sep 2009 Posts: 51 Thanks: 0  Find the differential dy
Find the differential dy of the given function. y = 7 sqrt(x)+ 1/sqrt(x) 
October 20th, 2009, 02:23 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,596 Thanks: 938 Math Focus: Elementary mathematics and beyond  Re: Find the differential dy
Find dy/dx, then multiply both sides of the equation by dx.

October 20th, 2009, 03:15 PM  #3  
Senior Member Joined: Mar 2007 Posts: 428 Thanks: 0  Re: Find the differential dy Quote:
That is a good practice [technique] when doing implicit differentiation as well... 3x^2  5xy2 + y^3 ==> 6xdx  10xydy 5y^2dx + 3y^2dy = (6x  5y^2)dx + (3y^2  10xy)dy which can be written as a derivative wrt any other variable, even time ... ==> (6x  5y^2)[dx/dt] + (3y^2  10xy)[dy/dt] Or , if 3x^2  5xy2 + y^3 = 0 (6x  5y^2)dx + (3y^2  10xy)dy = 0 ==> dy/dx = ( 5y^2  6x)/(3y^2  10xy) Of course, when finding a derivative this way there would be only the one line written down in stages, not the several lines to demonstrate as above. One should never write bits and pieces, but the full expression when finding derivatives that way. Writing only as differentials, as initially, is quite legitimate.  

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