1. **Constant Rule:** The derivative of a constant is zero. Example: If $f(x)=5$, then $f'(x)=0$. 2. **Power Rule:** For $f(x)=x^n$, the derivative is $f'(x)=nx^{n-1}$. Example: If $f(x)=x^3$, then $f'(x)=3x^2$. 3. **Sum Rule:** The derivative of a sum is the sum of the derivatives. Example: If $f(x)=x^2+3x$, then $f'(x)=2x+3$. 4. **Difference Rule:** The derivative of a difference is the difference of the derivatives. Example: If $f(x)=x^3-x$, then $f'(x)=3x^2-1$. 5. **Product Rule:** For $f(x)=g(x)h(x)$, $f'(x)=g'(x)h(x)+g(x)h'(x)$. Example: If $f(x)=x^2 \cdot \sin x$, then $f'(x)=2x\sin x + x^2 \cos x$. 6. **Quotient Rule:** For $f(x)=\frac{g(x)}{h(x)}$, $f'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{(h(x))^2}$. Example: If $f(x)=\frac{x}{\cos x}$, then $f'(x)=\frac{1 \cdot \cos x - x(-\sin x)}{\cos^2 x}= \frac{\cos x + x \sin x}{\cos^2 x}$. 7. **Chain Rule:** For composite $f(g(x))$, the derivative is $f'(g(x)) \cdot g'(x)$. Example: If $f(x)=\sin(x^2)$, then $f'(x)=\cos(x^2) \cdot 2x$. 8. **Constant Multiple Rule:** The derivative of a constant times a function is the constant times the derivative. Example: If $f(x)=5x^3$, $f'(x)=5 \cdot 3x^2 = 15x^2$. 9. **Derivative of Exponential Function:** For $f(x)=e^x$, $f'(x)=e^x$. Example: If $f(x)=e^{3x}$, $f'(x)=e^{3x} \cdot 3 = 3e^{3x}$. 10. **Derivative of Logarithmic Function:** For $f(x)=\ln x$, $f'(x)=\frac{1}{x}$. Example: If $f(x)=\ln(5x)$, $f'(x)=\frac{1}{5x} \cdot 5 = \frac{1}{x}$.