Description
Convert a time derivative to a natural-log-time derivative.
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 time derivative to a natural-log-time derivative.
When to use this tool
Use Logarithmic Time Derivative Factor when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter time, derivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logTimeDerivative. Use the output convention below.
Convert a time derivative to a natural-log-time derivative. Require time > 0; logTimeDerivative = time*derivative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| time | Time | Required. Finite number; strictly above 0. |
| derivative | Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logTimeDerivative | Log Time Derivative | Required. Finite number. |
{
"input": {
"time": 4,
"derivative": 3
},
"output": {
"logTimeDerivative": 12
}
}Limitations and assumptions
- This uses d/d(ln t), not base-10 log time; derivative and time must describe the same variable/point.
- 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
- Logarithmic Derivative Residue Term
Return a logarithmic-derivative residue from zero/pole orders.
- Local Logarithmic Second Derivative
Return the local second logarithmic derivative.