Results 1 to 13 of 13

Math Help - Four Differentiation Questions

  1. #1
    Member
    Joined
    Oct 2006
    From
    Toronto
    Posts
    86

    Four Differentiation Questions

    The first ones obviously simple, I'm just not sure about the answer to the last two.


    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by SportfreundeKeaneKent View Post
    The first ones obviously simple, I'm just not sure about the answer to the last two.


    c) is just the quotient rule, but I don't use the quotient rule, so I will leave it for someone else to show you (I would do it
    using the product rule myself).

    e) g'(x) = 7/x -2 (3) e^(3x)

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,811
    Thanks
    701
    Hello, SportfreundeKeaneKent!

    I'll try the third one . . .


    . . . . . . . . . .(2x - 5)^3
    c) .g(x) . = . --------------
    . . . . . . . . . . (x + 1)^4


    . . . . . . . .(x + 1)^4 3(2x - 5)4x - (2x - 5)4(x + 1)
    g'(x) . = . -------------------------------------------------------
    . . . . . . . . . . . . . . . . . . . .(x + 1)^8


    . . . . . . .4(x + 1)(2x - 5) [3x(x + 1) - (2x - 5)]
    Factor: . --------------------------------------------------
    . . . . . . . . . . . . . . . . . (x + 1)^8


    . . . . . .4(2x - 5)(x + 3x + 5)
    . . . = . -----------------------------
    . . . . . . . . . . . (x + 1)^5

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2006
    From
    Toronto
    Posts
    86
    Is the answer to a.) y'= 18x^2-14x+4/x^1/3?

    and the answer to b.) f'(x)=4-12x or 4(1-3x)?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by SportfreundeKeaneKent View Post
    The first ones obviously simple, I'm just not sure about the answer to the last two.


    c): I will use the product rule, but you probably will want to use the
    quotient rule:

    dg/dx = 3 (2 x^2 - 5)^2 (4x) / (x+1)^4 + (2x^2-5)^3 (-4)/(x+1)^5

    ........= 4 (2 x^2-5)^2/(x+1)^4 [3x - (2x^2-5)/(x+1)]
    RonL
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2006
    From
    Toronto
    Posts
    86
    Could someone verify the second one b.) ? My friend and I are getting different answers even though there does not appear to be anything wrong with the way that either of us are doing the question.

    The answer which I got is 2sqrt(1-4x) - 4x-2/sqrt(1-4x)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by SportfreundeKeaneKent View Post
    Could someone verify the second one b.) ? My friend and I are getting different answers even though there does not appear to be anything wrong with the way that either of us are doing the question.

    The answer which I got is 2sqrt(1-4x) - 4x-2/sqrt(1-4x)
    b.) f(x) = (2x - 1)*(1 - 4x)^(1/2)

    f'(x) = 2*(1 - 4x)^(1/2) + (2x - 1)*(1/2)*(1 - 4x)^(-1/2)*(-4)

    I'll let you do the simplifying.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by SportfreundeKeaneKent View Post
    The answer which I got is 2sqrt(1-4x) - 4x-2/sqrt(1-4x)
    Correct. Be careful with parentheses on here:

    2*sqrt(1 - 4x) - (4x - 2)/(sqrt(1 - 4x))

    What answer did your friend get? They might be equivalent answers.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Oct 2006
    From
    Toronto
    Posts
    86
    Can I simplify that by finding the comon denominator to get this?:

    -12/sqrt(1-4x)
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    What program are you using to write the problem? Obviously it isn't Latex because the system is still down...
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Oct 2006
    From
    Toronto
    Posts
    86
    The other answer is 4-12x/sqrt1-4x

    I think that that one is right, not sure though.

    And qbrk, I don't know how to use that program so...
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by SportfreundeKeaneKent View Post
    Can I simplify that by finding the comon denominator to get this?:

    -12/sqrt(1-4x)
    No, but you can simplify it to:

    (4 - 12x)/sqrt(1 - 4x)
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by SportfreundeKeaneKent View Post
    The other answer is 4-12x/sqrt1-4x
    Correct. These answers are equivalent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differentiation Questions
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 1st 2011, 12:40 AM
  2. Differentiation Questions
    Posted in the Calculus Forum
    Replies: 13
    Last Post: February 13th 2011, 12:38 PM
  3. differentiation and several other questions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 19th 2010, 04:24 PM
  4. More Differentiation Questions
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: December 14th 2009, 09:46 PM
  5. Differentiation Questions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 14th 2009, 02:35 AM

Search Tags


/mathhelpforum @mathhelpforum