Description
Return partial elasticity at a supplied multivariable point.
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 partial elasticity at a supplied multivariable point.
When to use this tool
Use Calculus: Partial Elasticity At Supplied Point when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter x, functionValue, partialDerivative. 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 partial elasticity at a supplied multivariable point. Require functionValue != 0; elasticity = x*partialDerivative/functionValue.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| functionValue | Function Value | Required. Finite number. |
| partialDerivative | Partial Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.elasticity | Elasticity | Calculated result member: number. |
{
"input": {
"x": 2,
"functionValue": 4,
"partialDerivative": 3
},
"output": {
"result": {
"elasticity": 1.5
}
}
}Limitations and assumptions
- The derivative holds other inputs fixed and uses the same x coordinate; no function evaluation or broader sensitivity model is 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
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
- Second Order Relative Elasticity
Return a supplied second-order relative elasticity term.
- Local Relative Condition Number From Derivative
Return a local relative condition number from a derivative.