Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 400 off


if y=x+1/y prove that (x2-y2+3)dy/dx=1

5 years ago


Answers : (2)


Dear Aritra,

Solution:-  y = x +1/y.................(1)

              dy/dx = 1 - (1/y2) (dy/dx)

           [1 + (1/y2)] (dy/dx) = 1..................(2)

        From eq. (1), y-1/y = x. On squaring both sides, we get-

 (y-1/y )2= x2 or  y2 + 1/y2 -2= x2 or 1/y2 = (x2 - y2+2)

Putting the value of 1/y2  in eq. (2), we get-

  [1 + (x2 - y2+2)] (dy/dx) = 1

(x2 - y2+3) (dy/dx) = 1

Hence proved.                       

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.

All the best Aritra!!!

Askiitians Experts
Priyansh Bajaj

5 years ago

x=y-1/y ...........1

differentiating wrt x

 1 = dy/dx -1/y2 (dy/dx)

dy/dx=y2 /1+y2  ................2

we have to prove (x2 -y2 +3 )dy/dx =1       or

                      x2 -y2 +3 =1/(dy/dx)

taking LHS

                    = (x-y)(x+y)+3                     (putting x from eq 1)

                   = y2 +1/y2  .....................4

taking RHS

                     =1/(dy/dx)=(y2+1)/y2 .............5

FROM 4 & 5


hence proved


5 years ago

Post Your Answer

Other Related Questions on Differential Calculus

Consider a curve y=f(x)We know that dy/dx = f ‘ (x) Now What is the geometrical meaning of dy/dx ?
it refers to the very very small interval of that postion w.r.t itself. Limiting the change in time to 0 sec.
mahima pareek 2 months ago
(d/dx)((2x)/(3x))? what is the value of this a)1 b)2/3 c)0 d)3/2
0 is the answer.. i am damn sure 0 is the answer.. hey i am fillin g this as rubbish because i have to have 100 characters.. anyways it is 0 because 2x/3x is 2/3.. derivative of constant is ...
Jayakrishna Natarajan 9 months ago
here the answer is zero because here 2x/3x here x and x is cancel so after here 2/3 so the answer is 0
murali 8 months ago
Let f : [a, b] → R be continuous on [a, b] and differentiable on (a, b). Suppose that f(a) = a and f(b) = b. Show that there is c ∈ (a, b) such that f′(c) = 1. Further, show that there are...
BY LMVT(Lagrange mean value theorem) Apply theorem in at points (a,f(a)) & (b,f(b)) This prove the first part that there exist a point c between a & b such that SECOND PART now break the...
Aakash one year ago
My answer was exactly the same as of Akash. But you disapproved my answer.
Anoopam Mishra one year ago
This is not fair!!!!!
Anoopam Mishra one year ago
trigonometric ratios of sub multiple angles: tan theta
trigonometric ratios of sub multiple angles: tan theta are: tan2A = 2tanA/(1-tan^2A) tanA = root((1-cos2A)/(1+cos2A)) tan3A = (3sinA – 4sin^3A)/(4cos^3A – 3cosA)
Vikas TU 2 months ago
FIND DOMAIN:- 1.sqrt cos(sinx) 2.sqrt sin(cosx) 3.1/sqrt 1+2sinx
For finding out the domain of the sqrt function, is should only take care of the condition that anything inside the sqrt should be always greater then or equal to positive only. It...
Vijay Mukati 3 months ago
0 to 2pi ,,,,pi/2 to -pi/2 these are the answers to the first two questions... similarly solve the third question and obtain the domain. always remember that denominator not equal to zero...
Rishabh Ranjan Das 3 months ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 400 off

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details