Type your implicit equation and compute dy/dx fast. Review partial derivatives, then download reports easily. Works on desktop, tablet, and mobile without visual clutter.
| Implicit Equation | dy/dx (Expected Form) | Sample Point | Slope at Point |
|---|---|---|---|
| x^2 + y^2 = 25 | -(2*x)/(2*y) | (3, 4) | -0.75 |
| x*y + y = 7 | -(y)/(x + 1) | (2, 2.3333) | -0.7778 |
| sin(x) + y^3 = 0 | -(cos(x))/(3*y^2) | (0, 0) | undefined |
| exp(y) + x = 0 | -(1)/(exp(y)) | (-1, 0) | -1 |
| x^2*y + ln(y) = 4 | -(2*x*y)/(x^2 + 1/y) | (1, 1) | -1 |
Start with an implicit relationship written as F(x,y)=0. When y depends on x, the total derivative is:
Solving for the slope gives: dy/dx = −(∂F/∂x)/(∂F/∂y). The calculator computes the two partial derivatives symbolically, then forms the ratio.
This calculator accepts either “LHS = RHS” or “F(x,y)=0” forms. It normalizes spacing and common operator symbols, then converts to F(x,y)=LHS−RHS for consistent processing. Equations up to 500 characters are supported, with parentheses and powers using ^. Use x and y, plus constants like pi and e, to keep evaluation deterministic.
Implicit differentiation uses total differentiation: dF/dx = Fx + Fy·(dy/dx). The tool computes Fx and Fy symbolically with product, quotient, chain, and power rules, including exp, trigonometric, and inverse‑trigonometric functions. It then isolates dy/dx = −Fx/Fy and optionally simplifies using constant folding and identities such as multiplying by 1, adding 0, and reducing powers like u^1.
The numeric slope at a point is reliable when Fy(x0,y0) ≠ 0. If Fy approaches zero, dy/dx can become large, indicating a near‑vertical tangent or that the curve fails the local “function of x” test. In practice, compare both Fx and Fy: large |Fx| with tiny |Fy| signals steepness, while both near zero may indicate a cusp, intersection, or a point where the implicit curve is not smooth.
Many functions impose domain limits: ln(u) requires u>0, sqrt(u) requires u≥0, and division requires nonzero denominators. When a supplied point violates a domain, the calculator reports non‑finite values rather than masking the issue. Try a nearby point on the curve, refine your equation, or keep the output symbolic until you confirm valid coordinates from your problem data.
The interactive plot draws the zero‑contour F(x,y)=0 over a chosen rectangle, using a configurable grid (typically 25–90 steps per axis). A denser grid produces smoother curves but increases computation time. If you provide (x0,y0) and a defined slope, the plot overlays the point and a tangent segment, helping you confirm sign changes and local behavior without manual sketching.
CSV export fits quick spreadsheet checks, while PDF export produces a compact record of F, partials, and dy/dx. For consistent comparisons across revisions, keep the same plotting window and record the evaluation point. In coursework and reports, pairing the symbolic dy/dx with a numeric slope strengthens validation and reduces transcription errors.
Yes. If you enter a single expression, the calculator treats it as F(x,y)=0. For example, x^2+y^2-25 is interpreted as x^2+y^2-25=0.
Implicit differentiation uses total differentiation. The slope is computed from dy/dx = −(∂F/∂x)/(∂F/∂y). Showing both partials helps you verify the rules applied and spot simplification opportunities.
It usually means ∂F/∂y evaluates to 0 at that point, so the curve has a vertical tangent or y is not locally a function of x. Try another point or analyze the curve geometry.
Start with a window that contains your expected solution, such as x from −10 to 10 and y from −10 to 10. If the curve looks clipped, widen the range or increase the grid resolution for smoother contours.
Common functions are supported, including sin, cos, tan, exp, ln, sqrt, abs, and inverse trig functions. Use parentheses and ^ for powers. For two‑argument powers, use pow(a,b).
If you provide both x and y and the slope is finite, exports include the evaluated dy/dx at that point. If evaluation fails due to domains or division by zero, the exports show the symbolic derivative and omit the numeric value.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.