Page 1 of 2 12 LastLast
Results 1 to 15 of 17
Like Tree2Thanks

Math Help - How do I find the derivative of this problem?

  1. #1
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    How do I find the derivative of this problem?

    f(x)=x2+2(3x2−3)(x2−2)





    Do I just multply out the top to get f(x) and then get the derivative by the quotient rule from there?

    I got what I thought was the derivative: (12x^2(X^2+2)-(3x^2-3)(x^2-2)(2x))/(x^2+2)^2 but it said I was incorrect.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,527
    Thanks
    773

    Re: How do I find the derivative of this problem?

    Quote Originally Posted by rhcprule3 View Post
    f(x)=x2+2(3x2−3)(x2−2)

    Do I just multply out the top to get f(x) and then get the derivative by the quotient rule from there?
    There is no top or bottom in what you have written; the whole formula is on one line.

    In plain text, it is customary to write x^2 for x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,530
    Thanks
    1387

    Re: How do I find the derivative of this problem?

    You seem to have forgotten a "/"! Did you mean (x^2+ 2)(3x^2- 3)/(x^2- 2)?
    (You also seem to have forgotten the parentheses around x^2+ 2. Or did you really mean "x^2+ [2(3x^2- 3)]= x^2+ 6x^2- 6= 7x^2- 6 as you wrote?)

    By the quotient rule, the derivative is [((x^2+2)(3x^2- 3))'(x^2- 2)- (x^2+2)(3x^2-3)(x^2- 2)']/(x^2-2)^2.
    You can do the derivative of the numertor, ((x^2+2)(3x^2- 3))' either by first multiplying it out or by using the product rule.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    Re: How do I find the derivative of this problem?

    sorry the problem was supposed to be (3x^2-3)(x^2-2) all over (x^2+2)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: How do I find the derivative of this problem?

    Quote Originally Posted by rhcprule3 View Post
    sorry the problem was supposed to be (3x^2-3)(x^2-2) all over (x^2+2)
    Use logarithmic differentiation: y' = \frac{{(3{x^2} - 3)({x^2} - 2)}}{{\left( {{x^2} + 2} \right)}}\left[ {\frac{{6x}}{{(3{x^2} - 3)}} + \frac{{2x}}{{({x^2} - 2)}} - \frac{{2x}}{{({x^2} + 2)}}} \right]
    Thanks from votan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: How do I find the derivative of this problem?

    Quote Originally Posted by rhcprule3 View Post
    sorry the problem was supposed to be (3x^2-3)(x^2-2) all over (x^2+2)
    y = (3x^2-3)(x^2-2)/(x^2+2)
    This is of the form y = u/v ==> (vu' - v'u)/v^2

    Can you continue from there?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,530
    Thanks
    1387

    Re: How do I find the derivative of this problem?

    Plato's point being that if y= \frac{(3x^2-3)(x^2- 2)}{x^2+ 2} then ln(y)= ln\left(\frac{(3x^2-3)(x^2- 2)}{x^2+ 2}\right)= ln(3x^2- 3)+ ln(x^2- 2)- ln(x^2+ 2) so that d(ln(y))/dx= (1/y)(dy/dx)= 6x/(3x^2- 3)+ 2x/(x^2- 2)- 2x/(x^2+ 2) and then
    dy/dx= [(3x^2- 3)(x^2- 2)/(x^2+ 2)]6x/(3x^2- 3)+ 2x/(x^2- 2)- 2x/(x^2+ 2)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    Re: How do I find the derivative of this problem?

    I've tried using the quotient rule to get the derivative but the webwork still says im incorrect
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: How do I find the derivative of this problem?

    Quote Originally Posted by rhcprule3 View Post
    I've tried using the quotient rule to get the derivative but the webwork still says im incorrect
    Show us your work we will help you finding what you missed
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,845
    Thanks
    715

    Re: How do I find the derivative of this problem?

    Quote Originally Posted by rhcprule3 View Post
    I got what I thought was the derivative: (12x^2(X^2+2)-(3x^2-3)(x^2-2)(2x))/(x^2+2)^2 but it said I was incorrect.
    Quote Originally Posted by rhcprule3 View Post
    I've tried using the quotient rule to get the derivative but the webwork still says im incorrect
    You have now been shown many different ways of finding the solution. If you got the answer wrong before, then try the quotient rule again. You did it wrong when you tried it before.

    Break it down. You have f(x) = \dfrac{u(x)}{v(x)}. Write out the functions u(x) and v(x). Then find the derivatives u'(x) and v'(x). Write them here for us to check, and we can figure out where you might be going wrong. From your answer in your first post, it appears you think the derivative of (3x^2-3)(x^2-2) is 12x^2. Is that the case?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    Re: How do I find the derivative of this problem?

    yes i believe the derivative is 12x^2 from u(x) and I belive the derivative for v(x) is 2x
    Last edited by rhcprule3; October 6th 2013 at 06:07 PM.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,845
    Thanks
    715

    Re: How do I find the derivative of this problem?

    Then that is your problem. If u(x) = (3x^2-3)(x^2-2), then u'(x) \neq 12x^2. Use the product rule (as HallsofIvy said).
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    Re: How do I find the derivative of this problem?

    Ive tried everything I got u'(x) to equal 12x^3-18x. So I did the quotient rule: (36x^2-18)(x^2+2)-2x(12x^3-18x) all over (x^2+2)^2. I've tried foiling and product rule on (36x^2-18)(x^2+2) but I still ended up with the wrong anser and its EXTREMELY frustrating!!!
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49

    Re: How do I find the derivative of this problem?

    You'll feel better when you realise that you've made errors, which is more reassuring than if the maths weren't capable of behaving itself! So re-read the given solutions. Here's another:



    ... 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).

    But this is wrapped inside the legs-uncrossed version of a triple version of...



    ... the product rule, where, again, straight continuous lines are differentiating downwards with respect to x.


    Full size


    __________________________________________________ __________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Thanks from IEE
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    Re: How do I find the derivative of this problem?

    Ive tried for f'(2) by plugging 2 for the x values but its still not giving it to me.... even with the product rule youve told me to use...
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: November 26th 2012, 01:50 PM
  2. Replies: 4
    Last Post: October 17th 2012, 06:51 AM
  3. Find the derivative
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 23rd 2009, 08:57 AM
  4. How do I find the derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 29th 2008, 05:54 PM
  5. Replies: 2
    Last Post: March 15th 2007, 07:49 PM

Search Tags


/mathhelpforum @mathhelpforum