Implicit Differentiation Calculator
Differentiate implicit equations and solve for dy/dx with guided steps and visual explanations.
Examples: x^2 + y^2 = 25, xy = 4, x^3 + y^3 = 6xy
Results
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Theory & Formula
What Is Implicit Differentiation?
Implicit differentiation finds dy/dx when x and y are related by an equation F(x, y) = 0 rather than y = f(x).
How to Differentiate Implicitly
1. Write the implicit equation in the form F(x, y) = 0
2. Differentiate both sides with respect to x
3. Apply the chain rule to every y term
4. Collect dy/dx terms and solve for dy/dx
Example: Circle x² + y² = 25
Differentiate x² + y² = 25 with respect to x.
\(x^2 + y^2 = 25\)\(\frac{d}{dx}(x^2) + \frac{d}{dx}(y^2) = \frac{d}{dx}(25)\)\(2x + 2y\frac{dy}{dx} = 0\)\(\frac{dy}{dx} = -\frac{x}{y}\)
Chain Rule Reminder
Because y depends on x, d/dx [yⁿ] = n·yⁿ⁻¹·dy/dx. Always multiply by dy/dx when differentiating y terms.
\(\frac{d}{dx}(y^n) = ny^{n-1}\frac{dy}{dx}\)