Comprehensive Differentiation Formulas & Rules Dataset
This dataset provides a comprehensive collection of 57 common differentiation formulas and rules, including basic rules, power rules, trigonometric functions, and more. Each entry lists the function, its derivative, conditions, and notes.
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💡 Key Takeaways
- Access 57 essential differentiation formulas and derivative rules.
- Explore calculus concepts with categorized functions and their derivatives.
- Download ready-to-use data for academic study or professional reference.
- Leverage detailed conditions and notes for each differentiation rule.
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⚠️ Showing first 20 of 57 records. Download the file for complete data.
| Category | Function f(x) | Derivative f'(x) | Condition | Notes |
|---|---|---|---|---|
| Basic Rules | c (constant) | 0 | - | Constant rule |
| Basic Rules | x | 1 | - | Identity function |
| Basic Rules | c·f(x) | c·f'(x) | c is constant | Constant multiple rule |
| Basic Rules | f(x) + g(x) | f'(x) + g'(x) | - | Sum rule |
| Basic Rules | f(x) - g(x) | f'(x) - g'(x) | - | Difference rule |
| Basic Rules | f(x)·g(x) | f'(x)g(x) + f(x)g'(x) | - | Product rule |
| Basic Rules | f(x)/g(x) | [f'(x)g(x) - f(x)g'(x)]/[g(x)]² | g(x) ≠ 0 | Quotient rule |
| Basic Rules | f(g(x)) | f'(g(x))·g'(x) | - | Chain rule |
| Power | x^n | n·x^(n-1) | - | Power rule |
| Power | 1/x | -1/x² | x ≠ 0 | Same as x^(-1) |
| Power | 1/x^n | -n/x^(n+1) | x ≠ 0 | Negative power |
| Power | √x | 1/(2√x) | x > 0 | Square root |
| Power | ∜x (x^(1/n)) | 1/(n·x^((n-1)/n)) | x > 0 | nth root |
| Power | x^x | x^x(ln(x) + 1) | x > 0 | Logarithmic differentiation |
| Exponential | e^x | e^x | - | Natural exponential |
| Exponential | a^x | a^x·ln(a) | a > 0, a ≠ 1 | General exponential |
| Exponential | e^(f(x)) | e^(f(x))·f'(x) | - | Chain rule applied |
| Exponential | a^(f(x)) | a^(f(x))·ln(a)·f'(x) | a > 0 | General form with chain rule |
| Logarithmic | ln(x) | 1/x | x > 0 | Natural logarithm |
| Logarithmic | log_a(x) | 1/(x·ln(a)) | x > 0, a > 0 | General logarithm |
🔧 Use Cases
- Import the CSV file into your Python scripts or SQL database to build custom calculus learning applications or study tools.
- Use the Excel file to filter formulas by category, analyze conditions, or create study guides with ease.
- Print the PDF version for quick offline reference during exams, classroom lectures, or personal study sessions.
- Reference this dataset to quickly verify derivatives for complex functions in engineering, physics, or data science calculations.