Answer
$dy/dx=\frac{-18xy^2-42y}{18x^2y+42x-6}$
Work Step by Step
Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x:
$2(3xy+7)\times(3x\times\frac{dy}{dx}+3y)=6\times\frac{dy}{dx}$
$(6xy+14)(3x\times\frac{dy}{dx}+3y)=6\times\frac{dy}{dx}$
$18x^2y(dy/dx)+42x(dy/dx)+18xy^2+42y=6(dy/dx)$
Move all terms with dy/dx to one side of the equation, and isolate dy/dx:
$18x^2y(dy/dx)+42x(dy/dx)-6(dy/dx)=-18xy^2-42y$
$dy/dx=\frac{-18xy^2-42y}{18x^2y+42x-6}$
