Implicit differentiation allows the derivative of a function defined implicitly by an equation (rather than an explicit formula) to be computed by differentiating both sides of the defining equation with respect to the independent variable, applying the chain rule to terms involving the implicit function, and algebraically solving for the derivative. This derivative can then be combined with a known point on the curve to construct a linear (tangent-line) approximation, which estimates the implicit function's value near that point when no algebraic method exists to compute it directly. This belongs to differential calculus, connecting the theory of implicitly defined functions to the linear approximation method built from a function's value and derivative at a base point.
Implicit differentiation allows the derivative of a function defined implicitly by an equation (rather than an explicit formula) to be computed by differentiating both sides of the defining equation …