Calculate derivatives of implicit functions where y is not isolated. Master the Chain Rule application.
Definition
Derivative Result
-x/yDerivative
dy/dx Result
\frac{dy}{dx} = -\frac{x}{y}
Chain Rule Applied
Visualization Example
Tangents exist even where functions are vertical!
About this calculator
Introduction
Implicit differentiation allows you to find the slope of a curve dy/dx even when y cannot be written explicitly as a function of x (e.g., x² + y² = 25). We treat y as a function of x, apply the derivative to both sides, and use the Chain Rule for terms involving y.
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Pro Tips
Differentiate both sides with respect to x.
Multiply by y' (or dy/dx) whenever you differentiate a y term.
Collect all terms with y' on one side and factor it out to solve.
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Fun Facts
"This technique is essential for related rates problems in physics."
"It allows us to find tangent lines to complex shapes like the Folium of Descartes."
