Description
Require forwardDerivative nonzero and return its reciprocal as inverseDerivative.
A derivative or error component is local to its stated variables and formula. A reciprocal derivative requires a nonzero slope, while a relative error requires a defined reference denominator.
Require forwardDerivative nonzero and return its reciprocal as inverseDerivative.
When to use this tool
Use Inverse Function Local Derivative when you need one local calculus or error-analysis component from supplied values.
How to use the tool and how it works
- Enter forwardDerivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read inverseDerivative. Use the output convention below.
Require forwardDerivative nonzero and return its reciprocal as inverseDerivative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| forwardDerivative | Nonzero local derivative dy/dx; the reciprocal is dx/dy only under the stated inverse-function assumptions. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| inverseDerivative | Reciprocal of the nonzero supplied forward derivative; local inverse-function assumptions are not checked. | Required. Finite number. |
{
"input": {
"forwardDerivative": 4
},
"output": {
"inverseDerivative": 0.25
}
}Limitations and assumptions
- This is a local inverse-derivative term under the inverse-function assumptions; the function, inverse existence, differentiability, and matching evaluation point are not verified.
- 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 underlying function, differentiability, domain, and complete error model separately.
References
Similar or alternative tools
- Linear Bracket Local Coordinate
Require increasing nodes and query within them, then return (query-leftNode)/(rightNode-leftNode).
- Linearization Relative Error
Require actualValue nonzero and return abs((linearizedValue - actualValue)/actualValue).