Implicit Differentiation Calculator
Calculate derivatives using implicit differentiation
About this calculator
This implicit differentiation calculator helps you find derivatives of functions that cannot be easily solved for y in terms of x. Unlike explicit functions where y = f(x), implicit functions involve both x and y variables mixed together, such as x² + y² = 25 or xy + sin(y) = x. The calculator automatically applies the chain rule and treats y as a function of x, making it invaluable for solving complex calculus problems involving circles, ellipses, and other curved relationships.
How to use
Enter your implicit equation in the input field, using standard mathematical notation (x^2 for x², sin(y) for sine of y, etc.). Specify which variable you want to differentiate with respect to if needed. Click calculate to get the derivative dy/dx, which will be expressed in terms of both x and y variables.
Frequently asked questions
What types of equations can I use?
You can input any implicit equation containing x and y, including polynomials, trigonometric functions, exponentials, and logarithms like x² + y² = 25 or e^(xy) = x + y.
Why is my result in terms of both x and y?
Implicit derivatives naturally contain both variables because y cannot be isolated. The result dy/dx shows how y changes with respect to x at any point (x,y).
Can I find higher-order derivatives?
Yes, you can find second derivatives d²y/dx² by differentiating the first derivative result again, though this requires applying implicit differentiation rules repeatedly to the output.