Today I learnt about implicit differentiation using this:

$\frac{df}{dy}\times \frac{dy}{dx}$

I don't understand when doing implicit differentiation how the d/dy part works for y terms:

$\frac{d({y}^{2})}{dx}=\frac{d({y}^{2})}{dy}\times \frac{dy}{dx}=2y\frac{dy}{dx}$

Why is the derivative of y2 with respect to $y$, $2y$? Do you assume it's a function of something else? And similarly if you apply this same formula to an $x$ term (even though its not needed) you get:

$\frac{d({x}^{2})}{dx}=\frac{d({x}^{2})}{dy}\times \frac{dy}{dx}$

How does that simplify to the $2x$ I know it is?

$\frac{df}{dy}\times \frac{dy}{dx}$

I don't understand when doing implicit differentiation how the d/dy part works for y terms:

$\frac{d({y}^{2})}{dx}=\frac{d({y}^{2})}{dy}\times \frac{dy}{dx}=2y\frac{dy}{dx}$

Why is the derivative of y2 with respect to $y$, $2y$? Do you assume it's a function of something else? And similarly if you apply this same formula to an $x$ term (even though its not needed) you get:

$\frac{d({x}^{2})}{dx}=\frac{d({x}^{2})}{dy}\times \frac{dy}{dx}$

How does that simplify to the $2x$ I know it is?