Frequently Asked Questions

Implicit differentiation finds dy/dx for an equation relating x and y that isn't solved for y as an explicit function of x, such as x² + y² = 25.

It rewrites the equation as F(x, y) = 0, computes the partial derivatives ∂F/∂x and ∂F/∂y term by term, then applies dy/dx = −(∂F/∂x) / (∂F/∂y).

It comes from the implicit function theorem — differentiating F(x, y) = 0 with respect to x using the chain rule gives ∂F/∂x + (∂F/∂y)(dy/dx) = 0, which rearranges to dy/dx = −(∂F/∂x) / (∂F/∂y).

Standard polynomial terms in x and y with ^ for exponents, an = sign, and + or − between terms, such as x^2 + y^2 = 25 or 3x^2*y - y^3 = 4.

If ∂F/∂y = 0 at your point, the tangent line is vertical, and dy/dx is undefined at that exact location — this happens, for example, at the leftmost and rightmost points of a circle.

No — the point (x₀, y₀) is optional. Without it, you still get the general dy/dx formula; with it, you also get the numeric slope at that specific point.

For the slope to be meaningful for the curve, yes — the point should lie on the curve. The calculator evaluates the derivative at whatever (x₀, y₀) you enter regardless, so double-check the point satisfies your equation.

Yes — mixed terms are differentiated using the product rule automatically, since the tool tracks the power of x and y in every term separately.

Many curves — circles, ellipses, and more complex implicit curves — can't be algebraically solved for y as a single explicit function of x, so implicit differentiation is the only practical way to find the slope.

Yes, completely free with no sign-up, and it runs entirely in your browser.