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Find the implicit derivative $\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\left(1+2x\right)}=2x\right)$

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Implicit derivative of (x-y)^2 = x + y + 1

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https://www.youtube.com/watch?v=yUpDRpkUhf4

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https://www.youtube.com/watch?v=789aMeepbxI

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Implicit derivative of e^(xy^2) = x - y

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Implicit derivative of (x^2+y^2)^3 = 5x^2y^2

https://www.youtube.com/watch?v=1DcsREjyoiM
$\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\cdot\left(1+2x\right)}=2x\right)$

Time to solve it:

~ 0.24 seconds