10.3 Differentiating polynomials
To differentiate some algebra is required77 7 If you’re not confident in conducting algebraic manipulations (i.e. \saydoing algebra) then it really is worth spending time reviewing this; it’s foundational for everything else in mathematics.
Note that in the process of carrying out the expansion
We can then combine this with the rule for the derivatives of sums from above to find the derivatives of any polynomial.
For example, we can find the derivative of (which was the example used above).
Why is ?
Let’s suppose we have a function , then the derivative of is just