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\frac{d}{dx}\left(x^2 / \left(x + y\right)\right) = \frac{d}{dx}\left(y^2 + 6\right)

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Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=KyYC8XzKsHU

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Integral de x entre x^2+1, completando derivada (forma dv/v)

https://www.youtube.com/watch?v=Ti9Kq6KarFU

Pre-Calculus - Graphing rational functions using 5 steps, g(x) = (-3x^2 + x + 12) / (x^2 - 4)

https://www.youtube.com/watch?v=fG2HAWBNVNE

Algebra 2 - Dividing two rational expressions by factoring, ((x + y)/6) / ((x^2 - y^2)/3)

https://www.youtube.com/watch?v=mAn_OHWNj2c

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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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