Differentiation Rules

Rule 1

The derivative of a constant is zero.

Example

If 𝑓(𝑥)=𝑘, then 𝑓(𝑥)=0. If done graphically, observe the fact that the gradient does not change across every x-value.

Rule 2

If 𝑓(𝑥)=𝑥𝑛, then 𝑓(𝑥)=𝑛𝑥𝑛1.

Tip

This was covered in 6.03 - The Derivative of xⁿ in more detail.