If y=x^(1/2)+1/x^(1/2) the prove 2x dy/dx+y=2.x^(1/2)

Answers (1)

Solution: We  have , y= sqrtx+ frac1sqrtx              [ differentiate both side w.r.t x  ]

                             fracdydx=frac12sqrtx- frac12x sqrtx

put the value of   fracdydx   in the equation 2xfracdydx+y=2sqrtx                  ecause y=sqrtx+frac1sqrtx    

                                = 2x(frac12sqrtx-frac12xsqrtx)+sqrtx+frac1sqrtx

                                 = (sqrtx -frac1sqrtx)+sqrtx+frac1sqrtx=2sqrtx

 

                                 

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