Home
Class 12
MATHS
If v(x,y) = log((x^(2) +y^(2))/(x+y)), p...

If `v(x,y) = log((x^(2) +y^(2))/(x+y))`, prove that
`x(del v)/(del x) + y(del v)/(del y)=1`.

Text Solution

Verified by Experts

The correct Answer is:
`x (delv)/(delx) + y (del v)/(del y) =1.`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    PREMIERS PUBLISHERS|Exercise EXERCISE 8.8|15 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    PREMIERS PUBLISHERS|Exercise EXERCISE 8.6|9 Videos

  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Problem for practice|45 Videos

  • DISCRETE MATHEMATICS

    PREMIERS PUBLISHERS|Exercise Problems For Practice|30 Videos

Similar Questions

Explore conceptually related problems

If u(x,y) = (x^(2) + y^(2))/sqrt(x+y) , prove that x(del u)/(del x) + y(del u)/(del y) = 3/2 u .

If u = log ((x ^(2) y + y ^(2) x)/(xy)) then x (del u)/( del x) + y (del u)/(del y)=

If f(x,y) =2x^(3) - 11x^(2)y + 3y^(3) , prove that x(del f)/(del x) + y(del f)/(del y)=3f .

If u= tan^(-1) ((x^(3) + y^(3))/(x-y)) , Prove that x(del u)/(del x) + y(del u)/(del y) = sin 2u .

If f=x/(x^(2) + y^(2)) , then show that x (del f)/(del x) + y(del f)/(del y) =-f .

If u = cos ^(-1) ((x)/(y)) prove that x (del u)/(delx) + y (del u)/(dely)=0.

If v(x,y) = log (e^(x) + e^(y)) , then (del v)/(del x) + (del v)/(del y) is equal to

If w(x,y,z) = x^(2)(y-z) + y^(2)(z-x) + z^(2)(x-y) , then (del w)/(del x) + (del w)/(del y) + (del w)/(del z) is