| Rule | Function | Derivative |
|---|---|---|
| Constant multiplication | \( cf \) | \(cf’ \) |
| Power rule | \( x^n \) | \(nx^{x-1} \) |
| Sum rule | \( f + g \) | \(f’ + g’ \) |
| Difference rule | \( f - g \) | \(f’ - g’ \) |
| Product rule | \( f \times g \) | \(f’g + fg’ \) |
| Quotient rule | \( f/g \) | \(\ (f’g - fg’)/g^2 \) |
| Reciprocal rule | \( 1/f \) | \( −f’/f^2 \) |
| Chain rule | \( f \circ g \) | \( (f’ \circ g) \times g’ \) |
| Exponential | \( e^x \) | \( e^x \) |
| Exponential | \( a^x \) | \( a^x \ln(a) \) |
| Logarithms | \( \ln(x) \) | \( 1/x \) |
| Logarithms | \( \log_a(x) \) | \( 1/(x \ln(a)) \) |
| Trigonometry | \( \sin(x) \) | \( \cos(x) \) |
| Trigonometry | \( \cos(x) \) | \( -\sin(x) \) |
| Trigonometry | \( \tan(x) \) | \( \sec^2(x) \) |
| Inverse trigonometry | \( \sin^{-1}(x) \) | \( 1/\sqrt{1-x^2} \) |
| Inverse trigonometry | \( \cos^{-1}(x) \) | \( -1/\sqrt{1-x^2} \) |
| Inverse trigonometry | \( \tan^{-1}(x) \) | \( 1/(1+x^2) \) |