[(del y)/(del x)=?],[18y=sin-1((6x-4*sqrt(1-4x^(2)))/(5))]

Find (dy)/(dx) if y=sin^(-1)[(6x-4sqrt(1-4x^(2)))/(5)]

Find dy/dx if y = sin^-1[(6x-4sqrt(1-4x^2))/5]

Find (del f)/(del x), (del f)/(del y),(del^(2) f)/(delx^(2)), (del^(2) f)/(del y^(2)) , at x=2, y=3 if f(x,y) =2x^(2) + 3y^(2) - 8xy .

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 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).

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 y=f(x+ct)+g(x-ct), then show that (del^(2)y)/(del t^(2))=c^(2)(del^(2)y)/(del x^(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)