Results 1 to 5 of 5
Like Tree3Thanks
  • 1 Post By MarkFL
  • 1 Post By tom@ballooncalculus
  • 1 Post By kraj8995

Math Help - Chain rule/Derivative Calculation

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Hawaii
    Posts
    9

    Chain rule/Derivative Calculation

    Hi,
    Would anyone be able to tell me how I'd go about solving a problem like this. Are you taking the derivative of the entire problem or just the one in the parenthesis (f(4x^3))? The inclusion of (f) is also throwing me off, not sure if that's supposed to be part of the solution. Is the answer supposed be something like = 12x^2(f'(4x^3))? Any help on this would be greatly appreciated. Thanks! Ana

    Here's the problem . . .


    d/dx(f(4x^3)) = 6x^5

    Calculate f'(x) = ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Chain rule/Derivative Calculation

    We are given:

    \frac{d}{dx}\left(f\left(4x^3 \right) \right)=6x^5

    Using the chain rule, we find:

    f'\left(4x^3 \right)\cdot12x^2=6x^5

    f'\left(4x^3 \right)=\frac{x^3}{2}=\frac{4x^3}{8} hence:

    f'(x)=\frac{x}{8}
    Thanks from phenol
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49

    Re: Chain rule/Derivative Calculation

    Just in case a picture helps...



    ... where (key in spoiler) ...

    Spoiler:





    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    The general drift is...





    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; September 27th 2012 at 02:29 AM.
    Thanks from phenol
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2012
    From
    Hawaii
    Posts
    9

    Re: Chain rule/Derivative Calculation

    I've been trying to figure this problem out for about an hour now. Thanks so much for breaking it down step by step; and for the picture!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2012
    From
    Jaipur,Rajasthan
    Posts
    36
    Thanks
    1

    Re: Chain rule/Derivative Calculation

    The question is related to single derivative function. solving it as:
    (d(f(4x^3)/dx)=6x^5
    =>3*4x^2.f'(4x^3)=6x^5
    f('4x^3)=6x^5/12x^2
    =>f'(4x^3)=x^3/2
    =>f'(x)=x^3/(2*4x^2)
    =>f'(x)=x/8

    Derivative is defined as a measure of how a function changes as its input changes. This process of finding derivative is called differentiation.
    Last edited by skeeter; September 28th 2012 at 04:01 AM.
    Thanks from phenol
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: June 7th 2010, 12:44 AM
  2. Replies: 5
    Last Post: October 19th 2009, 02:04 PM
  3. Help with derivative of chain rule
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 30th 2008, 04:42 PM
  4. Replies: 2
    Last Post: December 13th 2007, 06:14 AM
  5. Chain Rule Derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 18th 2006, 08:20 PM

Search Tags


/mathhelpforum @mathhelpforum