Here are some examples:

- $$\frac{d}{dx}c=0$$Here $c$ is any constant.
- $$\frac{d}{dx}x=1$$
- $$\frac{d}{dx}x^{n}=n x^{n-1}$$
- $$\frac{d}{dx}e^x=e^x$$
- $$\frac{d}{dx}b^x=b^x ln(b)$$Here $b$ is any constant.
- $$\frac{d}{dx}arcsin(x)=\frac{1}{\sqrt{1-x^2}}$$
- $$\int x^n dx=\frac{x^{n+1}}{n+1}+C'$$

Well, that ought to suffice, I guess.