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If u = x^(4) + y ^(3) + 3x ^(2) y^(2) + ...

If `u = x^(4) + y ^(3) + 3x ^(2) y^(2) + 3x ^(2) y` find `(del u)/(delx), (delu)/(dely), (del^(2) u)/(delx^(2)) , (del^(2)u)/(delx dely).`

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PREMIERS PUBLISHERS-DIFFERENTIALS AND PARTIAL DERIVATIVES-PROBLEMS FOR PRACTICE
  1. Find dy if y = (x-2)/( 2x +3) for x =2, dx =1.

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  2. If u =x ^(2) + y ^(2) evaluate (del^(2)f)/(del x ^(2)) + (del ^(2) f)/...

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  3. If u (x,y) = (x ^(2))/( y)- (2y ^(2))/(x) then (del^(2) u)/(del x dely...

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  4. If f (x,y) is homogeneous function of degree 5 then x (del f)/(delx) +...

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  5. Computer the values of dy if f (y) =x ^(3) +x ^(2) -2x +1 where x chan...

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  6. use differentials to find the approximate value of root 3 65.

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  7. Find the differential dy for given x and dx, y = (x ^(2) +5) ^(3),x =1...

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  8. The approximate value of 1/(10.1).

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  9. If u = x^(4) + y ^(3) + 3x ^(2) y^(2) + 3x ^(2) y find (del u)/(delx),...

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  10. If u =x ^(3) +2xy^(2) -x ^(2)y show that (del^(2)u)/(delxdely) =(del^(...

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  11. If w = u^(2)e ^(v) where u = x/y, v = y log x find (delw)/(delx)

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  12. If u =sqrt(x ^(4) +y ^(4)) show that x (delu)/(delx) + y ( del u)/(del...

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  13. If w = e ^(xy) wh4ere x = t ^(2), y = t ^(3) show that (dw)/(dt)=5t ^(...

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  14. If w=xy + z, where x=cos t, y = sin t, z=t, find (dw)/(dt).

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  15. If u =tan^(-1)((x ^(4) +y ^(4))/(x ^(2)-y ^(2))) show that x (delu)/(d...

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  16. Find (26)^((1)/3)).

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  17. Find the value of x (del z)/(delx) + y (del z)/( dely) if z = log ((x ...

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  18. Verify Euler's theorem for w = x ^(2) sin ((y)/(x)).

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

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  20. If u = sin ((x)/(y)) prove that u (xy) = u (yz).

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