Description
Return the third product derivative from supplied component derivatives.
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 the third product derivative from supplied component derivatives.
When to use this tool
Use Product Rule Third Derivative Term when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter f, df, ddf, dddf, g, dg, ddg, dddg. 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 the third product derivative from supplied component derivatives. derivative = f'''*g+3*f''*g'+3*f'*g''+f*g'''.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| f | F | Required. Finite number. |
| df | Df | Required. Finite number. |
| ddf | Ddf | Required. Finite number. |
| dddf | Dddf | Required. Finite number. |
| g | G | Required. Finite number. |
| dg | Dg | Required. Finite number. |
| ddg | Ddg | Required. Finite number. |
| dddg | Dddg | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"f": 2,
"df": 3,
"ddf": 4,
"dddf": 5,
"g": 6,
"dg": 7,
"ddg": 8,
"dddg": 9
},
"output": {
"derivative": 204
}
}Limitations and assumptions
- All values must come from the same point and variable; this is formula evaluation rather than symbolic or numerical differentiation.
- 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
- Inverse Function Third Derivative
Return a third inverse-function derivative from supplied forward derivatives.
- Chain Rule Three Stage Local Product
Return a three-stage scalar chain-rule derivative.