Given the equation $\sqrt[\phantom{2}]{x^2+6xy+y^4}=2,$ evaluate $\frac{dy}{dx}.$ Assume that the equation implicitly defines $y$ as a differentiable function of $x.$

If $F(x,y)=\sqrt[\phantom{2}]{x^2+6xy+y^4}-2=0,$ then $F_x=$

If $F(x,y)=\sqrt[\phantom{2}]{x^2+6xy+y^4}-2=0,$ then $F_y=$

$\frac{dy}{dx}=$

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