Results 1 to 8 of 8
Like Tree1Thanks
  • 1 Post By Plato

Math Help - How do cosX and cos X and cos (X) all differ derivative wise?!

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    How do cosX and cos X and cos (X) all differ derivative wise?!

    How are CosX and Cos X and Cos (X) all differ derivative wise?!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Quote Originally Posted by skinsdomination09 View Post
    How are CosX and Cos X and Cos (X) all differ derivative wise?!
    Are you clear that \cos^2(x)~\&~\cos(x^2) are two different functions?

    Now many computer algebra systems use the notation \cos(x)^2 for what traditionally has been written as \cos^2(x).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Quote Originally Posted by Plato View Post
    Are you clear that \cos^2(x)~\&~\cos(x^2) are two different functions?

    Now many computer algebra systems use the notation \cos(x)^2 for what traditionally has been written as \cos^2(x).
    Yeah but what confuses me is cos x vs. cos (x). Are they different? When parenthesis aren't there I always get mixed up
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Quote Originally Posted by skinsdomination09 View Post
    Yeah but what confuses me is cos x vs. cos (x). Are they different? When parenthesis aren't there I always get mixed up
    Outside CAS no one uses \cos(x)^2. So there is no reason to be confused,

    The derivative of \cos^2(x) is -2\cos(x)\sin(x)~.

    The derivative of \cos(x^2) is -2x\sin(x^2)~.

    BTW. Because these are functions most of us insist that () be used.
    I will mark \cos~x as wrong.
    Last edited by Plato; October 1st 2012 at 03:07 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Quote Originally Posted by Plato View Post
    Outside CAS no one uses \cos(x)^2. So there is no reason to be confused,

    The derivative of \cos^2(x) is -2\cos(x)\sin(x)~.

    The derivative of \cos(x^2) is -2x\sin(x^2)~.
    Thanks but can you explain the cos(x) one. It doesn't quite look like either the product or chain so I'm slightly confused. Sorry to be so difficult
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Quote Originally Posted by Plato View Post
    Outside CAS no one uses \cos(x)^2. So there is no reason to be confused,

    The derivative of \cos^2(x) is -2\cos(x)\sin(x)~.

    The derivative of \cos(x^2) is -2x\sin(x^2)~.

    BTW. Because these are functions most of us insist that () be used.
    I will mark \cos~x as wrong.
    Sorry but when I look the top one I think chain rule. So i'd derive cos (the outside) and get -2sin and leave the inside the same so i'd end up with -2sin(X). Why is this wrong?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Quote Originally Posted by skinsdomination09 View Post
    Thanks but can you explain the cos(x) one. It doesn't quite look like either the product or chain so I'm slightly confused. Sorry to be so difficult
    If f is differentiable function then the derivative D_x(f^2(x))=2f(x)f^{\prime}(x).
    It is really the product rule because f^2(x)=f(x)\cdot f(x)~.
    Thanks from skinsdomination09
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    Re: How do cosX and cos X and cos (X) all differ derivative wise?!

    Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: August 28th 2012, 09:24 AM
  2. Replies: 11
    Last Post: June 16th 2011, 11:42 AM
  3. implicit differ...answer check
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 28th 2010, 04:55 PM
  4. Replies: 2
    Last Post: October 25th 2008, 04:19 PM
  5. Word Problem of Implicit Differ.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 21st 2008, 11:49 PM

Search Tags


/mathhelpforum @mathhelpforum