#### Differentiation Rules for Polynomials

- The other rules regarding differentiation such as addition, subtraction, multiplication, division of functions, chain rule etc. applies too.
- All of these rules can be proven via first principles, but it is not required.
- The only rule for differentiating polynomials:

\text { If } f(x)=x^{n}, \text { then } f^{\prime}(x)=n x^{n-1}

where n \neq 0, n \in R (or n \in R \backslash\{0\})

Note: If n=0, then f(x)=a \text { constant, } f^{\prime}(x)=0

Proof (Not required)