Implicit Derivative Calculator
Calculate the derivative dy/dx of an implicit equation. Enter an equation in x and y, set the order, and get step-by-step differentiation.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Implicit Derivative Calculator
- Enter an equation in the input field (e.g.,
x^2 + y^2 = 1). Use^for exponents and standard math operators (+,-,*,/). - Select the derivative order from the dropdown:
- 1st derivative (dy/dx) – for first-order implicit differentiation.
- 2nd derivative (d²y/dx²) – for second-order implicit differentiation.
- Click "Calculate" to compute the result.
- View the result displayed as
dy/dx = ...ord²y/dx² = ..., along with step-by-step derivation.
Tips:
- Use only
xandyas variables. Other letters are treated as constants. - Ensure the equation has exactly one equals sign (
=). - For multiplication, use
*(e.g.,2*x*y).
Previous Results
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Frequently Asked Questions
An implicit derivative is the derivative of a function defined implicitly by an equation in x and y, rather than explicitly as y = f(x). It is found by differentiating both sides of the equation with respect to x and then solving for dy/dx.
You can enter polynomial equations, trigonometric functions (sin, cos, etc.), exponentials, logarithms, and more. Use ^ for exponentiation, * for multiplication, and parentheses for grouping. The variable must be x or y.
The result shows dy/dx (first derivative) or d²y/dx² (second derivative) expressed in terms of x and y. The steps detail the differentiation process.
