Description
Convert a supplied derivative under affine coordinate scales.
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.
Convert a supplied derivative under affine coordinate scales.
When to use this tool
Use Derivative Under Affine Unit Change when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter derivative, inputScale, outputScale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read transformed. Use the output convention below.
Convert a supplied derivative under affine coordinate scales. Require inputScale != 0; transformed = derivative*outputScale/inputScale.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
| inputScale | Input Scale | Required. Finite number. |
| outputScale | Output-coordinate scale; slope changes by outputScale/inputScale, while offsets drop out. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| transformed | Transformed | Required. Finite number. |
{
"input": {
"derivative": 3,
"inputScale": 2,
"outputScale": 4
},
"output": {
"transformed": 6
}
}Limitations and assumptions
- Scales mean new input/output per old unit; additive offsets cancel, while actual units and transformation validity remain supplied.
- 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
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- Local Relative Condition Number From Derivative
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