Results 1 to 5 of 5

Math Help - derivative of trig function

  1. #1
    Junior Member
    Joined
    Dec 2010
    Posts
    52

    derivative of trig function

    need little help with this: First i must decide the inverse to:

    f(x)=1/cos(x)

    so i think the inverse will be : x = arccos(1/y) right ?

    then i need help with derivate it
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    \dfrac{1}{\cos(x)}=\sec(x)

    what is the derivative of \sec(x)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2010
    Posts
    52
    i think it will be tan(x)cos(x) ?

    but if the question is to find out the inverses derivate, donīt that mean that i must first get the inverse and then derivate the inverse, not 1/cos(x) ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Quote Originally Posted by paulaa View Post
    i think it will be tan(x)cos(x) ?

    but if the question is to find out the inverses derivate, donīt that mean that i must first get the inverse and then derivate the inverse, not 1/cos(x) ?
    Not necessarily. With the inverse trig functions, a very common procedure to find the derivative of the inverse trig functions is to use implicit differentiation. This is how, for example,

    \dfrac{d}{dx}\,\sin^{-1}(x)=\dfrac{1}{\sqrt{1-x^{2}}} is done.

    You have y=\sin^{-1}(x), implying that \sin(y)=x.

    Implicitly differentiating yields

    \cos(y)\,y'=1\quad\Rightarrow\quad y'=\dfrac{1}{\cos(y)}.

    Now, if you draw the correct triangle, you will see that

    \cos(y)=\sqrt{1-x^{2}}. (Or you can just use the Pythagorean theorem.)

    Does that help?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Also, 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 theta), 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...



    Here is how you could also allow for an inner function like 1/y.

    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

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

Similar Math Help Forum Discussions

  1. Derivative of a trig function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 20th 2010, 11:24 AM
  2. derivative of trig function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 7th 2009, 03:48 PM
  3. derivative of trig function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 11th 2009, 08:48 AM
  4. Derivative of a Trig Function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 22nd 2009, 04:27 PM
  5. derivative of trig function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 4th 2008, 08:07 PM

Search Tags


/mathhelpforum @mathhelpforum