Hey! Sign in to get help with your study questionsNew here? Join for free to post

Leibnitz Theorem

    • Thread Starter

    Hi, Im finding trouble trying to understand the Leibnitz theorem, can anyone help and just try simplifying it for me, Im just not getting it!:mad:

    I got these 2 questions:
    Use Leibnitz theorem to compute the 5th derivative of:
    a) x^3cos(x)
    b) x^2ln(x)


    This looks not fun. Is it the same as what this page is describing http://www.math.ohio-state.edu/~neva...formula_H6.pdf

    If so letting u(x) = x^3 and v(x) = cos(x), I'd then find the 1-5 th derivatives of each of them, then just stick it in that big sum formula.
    • Thread Starter

    Yeah we have to use the formula given at the top of the page but I dont really understand it.

    I'll try write out the first few stages of the first one then.

    You have  x^3 \cos x so split this into two (easily differentiable) functions  u(x) = x^ and  v(x) = \cos x . Find their 1st, 2nd, ..., 5th derivatives and just keep them somewhere handy.

    Now do you understand the sum notation? This is what you'd do using the formula (I'm not going to write it out, I don't know the symbols)

    Firstly, in the big sum, r = 0, and n = 5 because you want the 5th derivative.
    So you get (5C0 is 5 choose 0, the binomial thingy)
     5C0 \ x^3 \frac{d^5 (cos x)}{dx} = - x^3 \sin x
    And now r = 1 so
     5C1 \frac{dx^3}{dx} \frac{d^4 (cos x)}{dx^4} = 15x^2 \cos x
    And now do this for r= 2, 3, 4, and 5.
    Finally add up all those bits because its a sum. Hopefully some stuff cancels out too.

    It's just the same as using the binomial theorem but substituting in derivatives, what part of it don;t you understand
    • Thread Starter

    Yeahh I think I get it now, I jus wasnt sure about the 'r' and 'n' term things. Thanks alot though
    • Thread Starter

    Sebbie I think I get it now, thanks

    if you were to find the odd derivatives how would you do that?
Write a reply… Reply
Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: December 5, 2010
How many mugs of tea do you drink a day?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.