Derivative Formulas Cheat Sheet:
- Addition/substraction rule: $(f\pm g)’ = f’ \pm g’$
- Constant rule: $(cf)’ = cf’$
- Product rule: $(fg)’=f’g+fg’$ (前微後不微 加 後微前不微)
- Chain rule: $(f\circ g)’ = f’\circ g\cdot g’$ (前微乘後微)
- Quotient rule: $(\frac{f}{g})’ = \frac{f’g-fg’}{g^2}$ (上微減下微除以下面平方)
| Function $f(x)$ | Derivative $\frac{d}{dx} (f(x))$ |
|---|---|
| Constant ($c$) | $0$ |
| Power Rule ($x^n$) | $nx^{n-1}$ |
| Exponential ($a^x$) | $a^x\ln(a)$ |
| Natural Logarithm ($\ln(x)$) | $\frac{1}{x}$ |
| Sine ($\sin(x)$) | $\cos(x)$ |
| Cosine ($\cos(x)$) | $-\sin(x)$ |
| Tangent ($\tan(x)$) | $\sec^2(x)$ |
These are some of the fundamental derivative rules that are frequently used in calculus.