Implicit Differentiation Calculator
Compute the derivative dy/dx for an implicit equation F(x,y)=0 using implicit differentiation. Enter an equation in terms of x and y, and get the derivative step-by-step.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Implicit Differentiation Calculator
- Enter an equation in the form
F(x, y) = 0. For example,x^2 + y^2 - 1for a circle. Use^for exponents,*for multiplication, and standard functions likesin,cos,sqrt, etc. - Optionally, specify x and y values to evaluate the derivative at a specific point. Leave blank for a general result.
- Click "Calculate Derivative".
- Read the result: The calculator shows
dy/dx(the implicit derivative). If you provided x and y values, it also evaluates the derivative at that point and checks if the point satisfies the equation. - Review the step-by-step breakdown below the result to see how the partial derivatives were computed numerically.
Tip: Ensure your equation equals zero (e.g., x^2 + y^2 - 1 not x^2 + y^2 = 1). The calculator uses numeric differentiation, so results are approximate (6 decimal places).
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Frequently Asked Questions
Implicit differentiation is a technique to find the derivative of a function when it is not explicitly solved for one variable. It treats y as a function of x and differentiates both sides of the equation.
It numerically computes the partial derivatives ∂F/∂x and ∂F/∂y at a point using finite differences, then applies the formula dy/dx = - (∂F/∂x) / (∂F/∂y).
Yes, as long as the equation can be expressed as F(x,y)=0 and the function is differentiable. Enter the left-hand side of the equation (e.g., for x^2 + y^2 = 1, enter x^2 + y^2 - 1).
No, they are optional. If provided, the calculator evaluates the derivative at that point. If not, it computes a general derivative at a default point (1,1).
