When should I use implicit differentiation?

Use it when variables are related by an equation and isolating the dependent variable is difficult or would create multiple branches.

Why does dy/dx appear after differentiating y?

Because y depends on x. The chain rule multiplies the derivative with respect to y by dy/dx.

Can it find the slope at a point?

Yes. Include the relation and point. Check first that the point satisfies the original equation.

Purpose-built solver page

Implicit Differentiation Solver

Use this implicit differentiation solver when x and y are linked in one equation and y is not isolated. It emphasizes chain-rule factors, collecting dy/dx terms, and evaluating slope at a point.

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implicit differentiation solver

F(x,y)=0 → dy/dx

Implicit relations

Chain-rule factors

Solve for dy/dx

implicit differentiation solver

Solve your implicit differentiation problem

Enter your implicit differentiation problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.

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F(x,y)=0 → dy/dx

How to use the Implicit Differentiation solver

A complete prompt usually produces a more useful explanation than an isolated expression.

1
Enter the full relation
x² + y² = 25
Include both x and y terms and state whether you need dy/dx or dx/dy.
2
Differentiate both sides
2x + 2y · dy/dx = 0
Apply ordinary rules to x terms and the chain rule to every y term.
3
Collect derivative terms
2y · dy/dx = −2x
Move all terms containing the requested derivative to one side.
4
Isolate and check
dy/dx = −x/y
Factor out the derivative, solve for it, and verify any supplied point satisfies the relation.

Tip: ask for a named method, a domain, or a verification step when your course requires one.

implicit differentiation solver

Chain-rule factors

Attach dy/dx whenever a term involving y is differentiated.

d/dx [y²]→2ydy/dx

Step

What this Implicit Differentiation solver is designed for

The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.

Implicit relations

Differentiate both sides while treating y as a function of x.

Chain-rule factors

Attach dy/dx whenever a term involving y is differentiated.

Solve for dy/dx

Collect derivative terms and isolate the requested derivative.

Slope at a point

Substitute a valid point into the derivative expression after deriving it.

Example

Implicit Differentiation problems to try

These examples reflect common search intent and can be inserted into the solver as a starting point.

Example 1

Find dy/dx if x^2 + y^2 = 25

A circle relation showing why differentiating y^2 adds a dy/dx factor.

Example 2

Find dy/dx if x^3 + y^3 = 6xy

A relation with product terms and derivative terms on both sides.

Example 3

Find the slope at (3, 4) on x^2 + y^2 = 25

Derive first, then evaluate the slope at a point on the curve.

Common mistakes to watch for

A worked answer is most useful when you know which details are easy to lose along the way.

Forgetting dy/dx

Differentiating a y term with respect to x requires the chain rule.

Solving for y first unnecessarily

Implicit differentiation often avoids a complicated or multi-branch explicit formula.

Using an invalid point

Before evaluating slope, confirm that the point lies on the original relation.