You are Here: Home >< Maths

# Leibniz' theorem watch

1. By using Leibniz' theorem, show that the value of the nth derivative of at is given by .

Hmmmm...
I don't know how to do this.

Lets do it step by step using what we know already:

Leibniz' thereom:

So in this example, we let and

But now what? How do we know how much we have to diffrentiate it to?
2. Evaluate the first few derivatives of , and from there the pattern for the nth derivative of should be fairly obvious. Also, what is the nth derivative of for n > 3?
3. (Original post by GHOSH-5)
Evaluate the first few derivatives of , and from there the pattern for the nth derivative of should be fairly obvious. Also, what is the nth derivative of for n > 3?
hmmm so the nth derivative for is:

right?

and also, the first few derivatives for are:

The pattern... is that they get multiplied by -4?
but i still dont understand. please could you explain a bit more?
4. What is (3-n)! if n is > 3?
5. Sorry to steal the thread momentarially, but is 0! = 1 or 0?
6. (Original post by Rubgish)
Sorry to steal the thread momentarially, but is 0! = 1 or 0?
0!=1 by definition
7. I'm sorry, this is totally irrelevant but when I read 'Leibniz' I immediately thought it was a theory about those REALLY yummy chocolate buscuits. yum. Clearly it isn't. It's also pretty clear I don't do maths. Bye.
8. (Original post by hahaha_dontknow)
The pattern... is that they get multiplied by -4?
Yes, and hence:

.
but i still dont understand. please could you explain a bit more?
After you realise what the even simpler form of the nth derivative for is for n greater than 3, use Leibniz's theorem.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 4, 2010
Today on TSR

### Are you living on a tight budget at uni?

From budgets to cutbacks...

### University open days

1. University of Cambridge
Wed, 26 Sep '18
2. Norwich University of the Arts
Fri, 28 Sep '18
3. Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 29 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams