Implicit function
Implicit differentiation

In calculus, a method called implicit differentiation makes use of the chain rule to differentiate implicitly defined functions.

To differentiate an implicit function y (x), defined by an equation R (x, y) = 0, it is not generally possible to solve it explicitly for y and then differentiate. Instead, one can totally differentiate R (x, y) = 0 with respect to x and y and then solve the resulting linear equation for dy / dx to explicitly get the derivative in terms of x and y. Even when it is possible to explicitly solve the original equation, the formula resulting from total differentiation is, in general, much simpler and easier to use.
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