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Step-by-step calculus

Implicit Differentiation Calculator

Differentiate an equation without isolating y. Track the chain rule, collect derivative terms, and see where the result is valid.

Works in your browserSteps explainedVideo explanations

Learn the method

Keep y dependent on x

The extra dy/dx factor is what distinguishes implicit differentiation from treating y as a constant.

x2+y2=25⟹dydx=−xy(y≠0)x^2+y^2=25\quad\Longrightarrow\quad \frac{dy}{dx}=-\frac{x}{y}\quad(y\ne0)
Calculus formulas

Worked example

  1. 1Differentiate both sides: 2x+2y(dy/dx)=0.
  2. 2Collect the derivative term: 2y(dy/dx)=−2x.
  3. 3Divide by 2y to get dy/dx=−x/y, provided y≠0.

At (±5,0), this expression is undefined and the circle has a vertical tangent. Do not divide by a quantity without checking when it is zero.

What this implicit differentiation calculator does

  • Choose independent and dependent variables.
  • Apply the chain rule to every dependent-variable term.
  • Solve for the first or higher derivative and state singular cases.
  • Multivariable equations are not passed off as ordinary one-variable graphs or numeric checks.

How to use it

  1. Enter a function or equation, or use the formula keyboard or a photo.
  2. Check the variable and differentiation settings, then press Solve.
  3. Read the steps, ask a follow-up question, or create a video lesson from the result.

Questions about the implicit differentiation calculator

When does implicit differentiation work?

For F(x,y)=0, a differentiable local function y(x) is guaranteed near a point where F is continuously differentiable and F_y is nonzero. Points with F_y=0 need separate analysis.

Does this calculator show steps?

Yes. The solver explains the rules and intermediate expressions. AI can make mistakes; check the assumptions and each step.

Can I generate a video explanation?

After solving, choose Video lesson to generate a narrated whiteboard explanation. Generation is subject to the displayed quota.