Calculus Implicit Differentiation Help

Hello Everyone,

Here's the problem:

Find dy/dx by implicit differentiation.
sqrt(7x+y) = 9+(x^2y^2)

sqrt = square root
(x^2y^2) = x squared times y squared, just to clarify.

Thanks everyone, best answer given to first accurate answer.

sqrt(7x+y) = 9+(x^2y^2)

sqrt(7x + y) - x^2 y^2 - 9 = 0

dy/dx = - d/dx [ sqrt(7x + y) - x^2 y^2 - 9 ] / d/dy [ sqrt(7x + y) - x^2 y^2 - 9 ]

. . . - d/dx = - ( 7 / (2 sqrt(7x + y)) - 2 x y^2 )
. . . d/dy = (1 / (2 sqrt(7x+y)) - 2 x^2 y)

dy/dx = - ( 7 / (2 sqrt(7x + y)) - 2 x y^2 ) / (1 / (2 sqrt(7x + y)) - 2 x^2 y)

dy/dx = (7 - 4 x y^2 sqrt(7x + y)) / (4 x^2 y sqrt(7x + y) - 1)

(7x + y)^(1/2) = 9 + (x * y)^2
(1/2) * (7x + y)^(-1/2) * (7 * dx + dy) = 2 * (xy) * (x * dy + y * dx)


If (7x + y)^(1/2) = 9 + (xy)^2, then 1 / (9 + (xy)^2) = 1 / (7x + y)^(1/2)

(1/2) * (1 / (9 + (xy)^2)) * (7 * dx + dy) = 2 * (xy) * (x * dy + y * dx)
7 * dx / (18 + 2 * (xy)^2) + dy / (18 + 2 * (xy)^2) = 2x^2 * y * dy + 2xy^2 * dx
7 * dx / (18 + 2 * (xy)^2) - 2xy^2 * dx = 2x^2 * y * dy - dy / (18 + 2 * (xy)^2)
dx * (1 / (18 + 2 * (xy)^2)) * (7 - 2xy^2 * (18 + 2(xy)^2)) = dy * (1 / (18 + 2(xy)^2)) * (2x^2 * y * (18 + 2(xy)^2) - 1)
dx * (7 - 2xy^2 * (18 + 2(xy)^2)) = dy * (2x^2 * y * (18 + 2(xy)^2) - 1)
dy/dx = (7 - 36xy^2 - 4x^3 * y^4) / (36x^2 * y + 4x^3 * y^4 - 1)