Results 1 to 7 of 7

Math Help - Derivatives - product rule + chain rule

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    229

    Derivatives - product rule + chain rule

    I'm having trouble getting to the derivative of y = x^2 sqrt(x-2). Could someone kindly provide a step-by-step solution to the problem? The answer is x(5x - 8) / 2 sqrt(x-2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49
    Are you sure? Here's a pic - I'll edit details and quite possibly corrections...



    Actually, the chain rule here is kind of trivial, so we could just use the product rule alone...



    ... where...



    ... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and then, because of the product rule, the whole of the bottom is the derivative of the whole of the top.

    Notice I've tweaked the second balloon along the bottom, just for a common denominator.

    OK - where does that get us in view of your proposed answer? Have you checked question and answer? Maybe its me...


    __________________________________________

    Don't integrate - balloontegrate!

    http://www.ballooncalculus.org/examples/gallery.html

    http://www.ballooncalculus.org/asy/doc.html
    Last edited by tom@ballooncalculus; October 19th 2009 at 03:35 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    229
    What's the problem?

    If the provided answer caused some confusion, it should be: x(5x - 8) / (2 sqrt(x-2)) to be more specific.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49
    Sorry, should have thought to do an additional tweak for the same reason, then I wouldn't have been confused...



    So, yes, there we are. Maybe your mental blip was related to mine. Anyway, hope you like the balloons for tracing through the product rule process - if not, use the formula, of course.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2009
    Posts
    229
    Quote Originally Posted by tom@ballooncalculus View Post
    Sorry, should have thought to do an additional tweak for the same reason, then I wouldn't have been confused...



    So, yes, there we are. Maybe your mental blip was related to mine. Anyway, hope you like the balloons for tracing through the product rule process - if not, use the formula, of course.
    I'm sorry I find the balloons kind of confusing. How did you get 4x/2 from x^2?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49
    That was the additional tweak for the sake of the common denominator. (2x because it's the derivative of x^2, then I just doubled the top and bottom.)

    Don't be sorry! - find an approach that works for you...

    Cheers
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2009
    Posts
    229
    Ah I finally understand - thank you so much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: November 9th 2010, 02:40 AM
  2. Derivatives - product/quotient/chain rule
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 19th 2009, 07:02 PM
  3. Replies: 5
    Last Post: October 19th 2009, 02:04 PM
  4. Replies: 3
    Last Post: May 25th 2009, 07:15 AM
  5. Replies: 0
    Last Post: February 18th 2009, 11:12 PM

Search Tags


/mathhelpforum @mathhelpforum