Description
Return local slope for a supplied implicit equation F(x,y)=0.
An implicit relation defines local derivatives only where its smoothness and nonzero-partial hypotheses apply. Gradient and Hessian components supplied as numbers do not establish that a point lies on the level set or that a regular implicit function exists there.
Return local slope for a supplied implicit equation F(x,y)=0.
When to use this tool
Use Calculus: Implicit Two Variable Local Slope when evaluating the stated implicit-derivative or level-set term from supplied partial derivatives.
How to use the tool and how it works
- Enter partialX, partialY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return local slope for a supplied implicit equation F(x,y)=0. Require partialY != 0; slope = -partialX/partialY.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| partialX | Partial X | Required. Finite number. |
| partialY | Partial Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.slope | Slope | Calculated result member: number. |
{
"input": {
"partialX": 2,
"partialY": 4
},
"output": {
"result": {
"slope": -0.5
}
}
}Limitations and assumptions
- The point must lie on a sufficiently differentiable regular level set; the function, point and implicit-function hypotheses are not verified.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Check the original level-set equation, differentiability and the relevant implicit-function hypotheses before interpreting these local derivative formulas.
References
Similar or alternative tools
- Implicit Three Variable Partial Ratio
Return local partials for a supplied implicit graph z(x,y).
- Implicit Second Partial Diagonal Term
Return a second derivative for a supplied implicit planar curve.