An implicit differentiation calculator finds dy/dx for equations where y isn’t isolated, like x² + y² = 25 or x³ + y³ = 6xy. It differentiates both sides with respect to x, applies the chain rule to y terms and solves for dy/dx, showing every step.
The key idea: whenever you differentiate a term with y, multiply by dy/dx, because y depends on x. Example: x² + y² = 25. Differentiate both sides: 2x + 2y(dy/dx) = 0. Solve: dy/dx = −x/y. At the point (3, 4), the slope of the tangent line to the circle is −3/4.
A harder example: x³ + y³ = 6xy. Differentiate: 3x² + 3y²(dy/dx) = 6y + 6x(dy/dx), using the product rule on the right. Group dy/dx terms: (3y² − 6x)(dy/dx) = 6y − 3x². So dy/dx = (6y − 3x²) ÷ (3y² − 6x) = (2y − x²) ÷ (y² − 2x).
Common mistakes: forgetting dy/dx on y terms, forgetting the product rule on terms like xy, and algebra errors when solving for dy/dx. Implicit differentiation is also the basis for related rates problems, where you differentiate with respect to time and connect changing quantities.
Why use an online Implicit Differentiation Calculator: it saves time, avoids simple arithmetic mistakes and shows each step, so you can check your homework, plan a project or make a decision with confidence. Bookmark the page so it’s ready the next time you need it.
Tips for getting accurate results from the Implicit Differentiation Calculator: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
Learn more on Wikipedia’s implicit function article. Find partial derivative, L’Hôpital’s rule and critical number calculators on Minedit.