Implicit differentiation


Definition

In calculus, a method called 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 $y$ 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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