(del b" orads ")/(2x^(2)+7x+3)

If u = x ^ (2) tan ^ (- 1) ((y) / (x)) - y ^ (2) tan ^ (- 1) ((x) / (y)), prove that (del ^ (2) u) / (del x del y) = (x ^ (2) -y ^ (2)) / (x ^ (2) + y ^ (2))

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

If x = r cos theta and y = r sin theta, prove that (del ^ (2) r) / (del x ^ (2)) + (del ^ (2) r) / (del y ^ (2)) = (1) / (r) [((del r) / (del x)) ^ (2) + ((del r) / (del y)) ^ (2)]

If w(x,y) = xy + sin(xy) , then prove that (del^(2) w)/(del y del x) = (del^(2) w)/(del x del y)

If z (x + y) = x ^ (2) + y ^ (2) show that [(del z) / (del x) - (del z) / (del y)] ^ (2) = 4 [1 - (del z) / (del x) - (del z) / (del y)]

If v(x,y,z) = x^(3) + y^(3) + z^(3) + 3xyz , show that (del^(2)v)/(del y del z) = (del^(2)v)/(del z del y)

If u=log sqrt(x^(2) + y^(2)) , then (del^(2) u)/(del x^(2)) + (del^(2)u)/(del y^(2)) is

If u=log(x^(2)+y^(2)+z^(2)) prove that (del^(2)u)/(del x^(2))+(del^(2)u)/(del y^(2))+(del^(2)u)/(del z^(2) = 2/(x^(2)+y^(2)+z^(2)

If u (x,y) = (x ^(2))/( y)- (2y ^(2))/(x) then (del^(2) u)/(del x dely) - (del ^(2) u)/(dely delx) is :

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).