MathSimplify
Calculus

Implicit Differentiation

Find the derivative of implicit relations and functions. Get instant step-by-step solutions — completely free, no signup required.

Free Implicit Differentiation Calculator

Enter your problem below to get an instant step-by-step solution.

About Implicit Differentiation

Find the derivative of implicit relations and functions. Calculus is the mathematical study of continuous change. It provides tools for analyzing functions, computing areas and volumes, and solving differential equations that model real-world phenomena.

Our Implicit Differentiation calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any implicit differentiation expression and receive a complete, verified solution with every step shown.

Implicit Differentiation Formula

d/dx [y^n] = n·y^(n−1) · dy/dx

Implicit differentiation finds dy/dx when y is not written as an explicit function of x. Differentiate every term with respect to x, treating y as a function of x — so every derivative of a y-term picks up a factor of dy/dx by the chain rule — then solve for dy/dx.

Worked Example

Find dy/dx for x² + y² = 25

  1. Differentiate both sides: 2x + 2y·(dy/dx) = 0
  2. Isolate the dy/dx term: 2y·(dy/dx) = −2x
  3. Divide by 2y: dy/dx = −x / y
  4. At the point (3, 4) the slope is −3/4

Answer: dy/dx = −x / y

Common Mistakes to Avoid

  • Forgetting the dy/dx factor when differentiating y-terms.
  • Treating a product like xy as a single variable instead of using the product rule.
  • Not collecting all dy/dx terms on one side before factoring it out.

How to Use the Implicit Differentiation Calculator

  1. 1

    Enter your calculus expression (e.g., a function for Implicit Differentiation) into the input field

  2. 2

    Press Enter or click the Solve button to run the calculation

  3. 3

    Review the step-by-step solution that appears below the input

  4. 4

    Check the breakdown of each operation to understand the method

  5. 5

    Try a different problem to practice and build your understanding

Frequently Asked Questions

What is the Implicit Differentiation formula?

d/dx [y^n] = n·y^(n−1) · dy/dx. Implicit differentiation finds dy/dx when y is not written as an explicit function of x. Differentiate every term with respect to x, treating y as a function of x — so every derivative of a y-term picks up a factor of dy/dx by the chain rule — then solve for dy/dx.

Can you show a worked Implicit Differentiation example?

Find dy/dx for x² + y² = 25: Differentiate both sides: 2x + 2y·(dy/dx) = 0; Isolate the dy/dx term: 2y·(dy/dx) = −2x; Divide by 2y: dy/dx = −x / y; At the point (3, 4) the slope is −3/4. Answer: dy/dx = −x / y.

Is this Implicit Differentiation calculator free to use?

Yes — the Implicit Differentiation calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.

Can I use this for Implicit Differentiation homework and exam practice?

Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.

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