How implicit differentiation works
- Differentiate both sides of the equation with respect to \(x\).
- Every derivative of a \(y\)-term gets a factor of \(dy/dx\).
- Collect the \(dy/dx\) terms and solve for \(dy/dx\).
Implicit Derivative Calculator
Differentiate implicit equations involving x and y.
Use this calculator as a study checker
Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.
- Check the method before copying the answer.
- Use the examples below to test nearby problems.
- Read the calculus guides for worked explanations.
Solution
50 study checks todayEnter an expression or choose an example to calculate.
Implicit Derivative Examples
What this calculator is for
Implicit differentiation is used when y is not isolated as a function of x. It works directly with equations that mix x and y. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.
Manual example
- Problem: \(x^2+y^2=25\).
- Differentiate: \(2x+2y(dy/dx)=0\).
- Solve: \(dy/dx=-x/y\).
Common mistakes to avoid
- Forgetting the \(dy/dx\) factor after differentiating \(y^2\).
- Trying to isolate \(y\) when implicit differentiation is simpler.
- Not solving the final equation for \(dy/dx\).
When to double-check the result
Implicit results can depend on points or branches of a curve. Review the domain and any vertical tangent cases separately.