If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: AP®︎/College Calculus BC>Unit 11

Lesson 3: AP Calculus BC 2011

# 2011 Calculus BC free response #6c

Calculating the 6th derivative at 0 from the Taylor Series approximation. Created by Sal Khan.

## Want to join the conversation?

• Is there a difference between the words 'order' and 'degree' when looking at these types of equations?
• I'm not sure why you can't just take the 6th derivative of f(x) at 0 by hand especially because all the terms with x just go away. Or am I missing something?
• You could, but you would need to contend with multiple applications of the product rule, things can get messy and that is where errors can be made. Doing it that way is often called the "Brute Force" method. Nothing wrong with that.

In this case, the question, and its several sections, are leading you, step by step, to an analytic solution, which is yours for the taking. It is one thing to be able to do the "cookbook" calculations, that is, relying on the application of the rules of differentiation and integration that apply to a given situation, and quite another to start to get a feel for the meaning of what you are doing and the implications of those meanings which will help guide you to analytic solutions.

Don't get me wrong, I am not belittling "Brute Force". You need to be an expert at it and do it many times to start to get a feel for the concepts and implications I am talking about. I am also not belittling you either because you may not yet see the implications, or, if you do, chose not to use that knowledge. Everyone progresses at their own rate, the key is to keep working at it.

Many mathematicians like to joke that they are lazy, but that laziness is an admirable trait because it is actually an optimization of effort, meaning that you can quickly dispense with one problem so as to move on to another.
Great Question!
Keep Studying!