Results 1 to 6 of 6

Math Help - Check derivtives for correctness

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    27

    Check derivtives for correctness

    I have not done differential calculus for awhile. I reviewed my calc book, but I am still having some trouble. Could someone please check these derivatives?

    f(x) = e^x + 2^-^x + 2*cos(x)-6
     f'(x) = e^x + ln(2)*2^-^x - 2*sin(x)-0
     f'(x) = e^x + 2^-^x * ln(2) - 2*sin(x)


    g(x) = 2xcos(2x)-(x-2)^2
     g'(x) = 2x (d/dx* cos(2*x))+cos(2*x)*(d/dx* 2x) - 2(x-2)
     g'(x) = -2xsin(2x)(2)+cos(2x)*2-2(x-2)
     g'(x) = -4xsin(2x) + 2cos(2x) - 2(x-2)

     h(x) = e^x - 3x^2
     h'(x) = e^x - 3*2*x
     h'(x) = e^x - 6*x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by sedemihcra View Post
    I have not done differential calculus for awhile. I reviewed my calc book, but I am still having some trouble. Could someone please check these derivatives?

    f(x) = e^x + 2^-^x + 2*cos(x)-6
     f'(x) = e^x + ln(2)*2^-^x - 2*sin(x)-0
     f'(x) = e^x + 2^-^x * ln(2) - 2*sin(x)


    g(x) = 2xcos(2x)-(x-2)^2
     g'(x) = 2x (d/dx* cos(2*x))+cos(2*x)*(d/dx* 2x) - 2(x-2)
     g'(x) = -2xsin(2x)(2)+cos(2x)*2-2(x-2)
     g'(x) = -4xsin(2x) + 2cos(2x) - 2(x-2)

     h(x) = e^x - 3x^2
     h'(x) = e^x - 3*2*x
     h'(x) = e^x - 6*x
    Correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    The first one:

    (2^{-x} )'=-ln(2)2^{-x}

    The third one is correct.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,057
    Thanks
    1690
    [QUOTE=sedemihcra;606004]I have not done differential calculus for awhile. I reviewed my calc book, but I am still having some trouble. Could someone please check these derivatives?

    f(x) = e^x + 2^-^x + 2*cos(x)-6
     f'(x) = e^x + ln(2)*2^-^x - 2*sin(x)-0
     f'(x) = e^x + 2^-^x * ln(2) - 2*sin(x)
    The second term should be -2^{-x} ln(2) because of the - in the numerator.
    By the way, the it is simpler to get 2^{-x} using "braces": "2^{-x}" rather than "2^-^x".


    g(x) = 2xcos(2x)-(x-2)^2
     g'(x) = 2x (d/dx* cos(2*x))+cos(2*x)*(d/dx* 2x) - 2(x-2)
     g'(x) = -2xsin(2x)(2)+cos(2x)*2-2(x-2)
     g'(x) = -4xsin(2x) + 2cos(2x) - 2(x-2)
    Good!

     h(x) = e^x - 3x^2
     h'(x) = e^x - 3*2*x
     h'(x) = e^x - 6*x
    Good.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by Also sprach Zarathustra View Post
    The first one:

    (2^{-x} )'=-ln(2)2^{-x}

    The third one is correct.
    Good eye on the negative sign.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2010
    Posts
    27
    Thanks for all the help. Also thanks for getting back so quick.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving NFA Correctness
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 3rd 2011, 01:12 PM
  2. Correctness
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: September 27th 2009, 09:15 AM
  3. Program Correctness Problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 18th 2009, 06:07 PM
  4. Program Correctness Proof
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 24th 2009, 10:12 PM
  5. Correctness of a sample function
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 25th 2006, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum