Implicit Differentiation Calculator
Find dy/dx for implicit equations using the chain rule. Step-by-step solutions included.
Understanding Implicit Differentiation
When to Use
- •Equations where y cannot be easily isolated
- •Curves like circles, ellipses, hyperbolas
- •Mixed terms like xy², x²y, etc.
- •Transcendental equations (trig, exp with both x and y)
Key Rules
- •d/dx[y] = dy/dx (chain rule)
- •d/dx[y²] = 2y(dy/dx)
- •d/dx[xy] = y + x(dy/dx) (product rule)
- •Solve for dy/dx after differentiating
Common Implicit Derivatives Reference
Related Math Tools
Educational Note: This calculator demonstrates implicit differentiation techniques. For complex equations, verify results and ensure the point lies on the curve. Always check your work in academic settings.
About Implicit Differentiation Calculator - Dy/Dx Solver
Calculate derivatives using implicit differentiation. Find dy/dx for implicitly defined functions with complete step-by-step solutions.
Our **Implicit Differentiation Calculator** finds dy/dx for equations where y cannot be easily solved as a function of x. Enter your equation, and get the derivative with detailed step-by-step explanations. Essential for circles, ellipses, and other implicit curves. For tangent line applications, see our Tangent Line Calculator.
Implicit differentiation applies the chain rule to both sides of an equation, treating y as a function of x. This technique handles equations like x² + y² = r² (circles) and x³ + y³ = 6xy (folium of Descartes). Try our Log Calculator for logarithmic derivatives.
Beyond basic derivatives, our calculator shows each differentiation step clearly, helping students understand the chain rule and product rule applications. Perfect for calculus students and engineers working with implicitly defined surfaces.
Key Features
Why Use This Tool?
Common Use Cases
Calculus: Learn implicit differentiation technique.
Geometry: Find slopes on circles and ellipses.
Related Rates: Problems where variables depend on time.
Engineering: Curves defined by implicit equations.
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How to Use
Enter the left side of your equation
Enter the right side (or constant)
Click Calculate
View dy/dx result and all steps