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Implicit differentiation is a technique used in calculus to find the derivative of a function that is defined implicitly. This means the function is not explicitly written in the form y = f(x), but rather in a form where y is related to x in a more complex way, such as F(x, y) = 0. The core idea is to differentiate both sides of the equation with respect to x, treating y as a function of x. When differentiating terms involving y, the chain rule is applied, meaning the derivative of y with respect to x (dy/dx or y') is multiplied by the derivative of the term with respect to y.

After differentiating both sides of the equation, the resulting equation will typically contain both x, y, and dy/dx. The next step is to algebraically isolate dy/dx. This usually involves gathering all terms containing dy/dx on one side of the equation and all other terms on the opposite side, followed by factoring out dy/dx and then dividing to solve for it. Implicit differentiation is particularly useful for finding the slope of a tangent line to a curve defined by an implicit equation at a given point. It simplifies the process when solving for y explicitly would be difficult or impossible.