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

 

                                 

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout NEET (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions