Description
Return derivative of a normalized scalar share.
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 derivative of a normalized scalar share.
When to use this tool
Use Derivative Of Normalized Scalar Pair when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter first, second, firstDerivative, secondDerivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Return derivative of a normalized scalar share. Require first+second != 0; derivative = (firstDerivative*second-first*secondDerivative)/(first+second)².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number. |
| second | Second | Required. Finite number. |
| firstDerivative | First Derivative | Required. Finite number. |
| secondDerivative | Second Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"first": 2,
"second": 3,
"firstDerivative": 1,
"secondDerivative": 0
},
"output": {
"derivative": 0.12
}
}Limitations and assumptions
- This differentiates first/(first+second); signed inputs are allowed, and no probability or underlying functions are 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
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
- Scalar Composition Second Derivative Term
Return the second derivative of a supplied scalar composition.
- Inverse Function Third Derivative
Return a third inverse-function derivative from supplied forward derivatives.