Description
Return a supplied second-order relative elasticity term.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return a supplied second-order relative elasticity term.
When to use this tool
Use Second Order Relative Elasticity when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter input, value, secondDerivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read elasticity. Use the output convention below.
Return a supplied second-order relative elasticity term. Require value != 0; elasticity = input²*secondDerivative/value.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| input | Input | Required. Finite number. |
| value | Value | Required. Finite number. |
| secondDerivative | Second Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| elasticity | Elasticity | Required. Finite number. |
{
"input": {
"input": 2,
"value": 4,
"secondDerivative": 2
},
"output": {
"elasticity": 2
}
}Limitations and assumptions
- Units and derivative variable must match; this is not the second derivative of log(value) or a complete response model.
- 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
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
Similar or alternative tools
- Calculus: Partial Elasticity At Supplied Point
Return partial elasticity at a supplied multivariable point.
- Local Relative Condition Number From Derivative
Return a local relative condition number from a derivative.