Results 1 to 4 of 4

Math Help - Derivative of trig functions under the natural log

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    2

    Derivative of trig functions under the natural log

    Could someone please help me figure out the first and second derivative of the following function:

    f(x)=ln(sec(6x)+tan(6x))

    Explanation would be very appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Standard Chain Rule: \dfrac{d}{dx} \ln[f(x)] = \dfrac{f'(x)}{f(x)}

    In this case you have f'(x) = \dfrac{\frac{d}{dx} \sec(6x) + \frac{d}{dx} \tan(6x)}{\sec(6x) + \tan(6x)}


    You'll need to use the chain rule again on the numerator
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,865
    Thanks
    744
    Hello, bennettb6!

    \text{Find the first and second derivative of the following function:}

    . . f(x)\:=\:\ln(\sec6x+\tan6x)

    Chain Rule: . \displaystyle f'(x) \;=\;\frac{1}{\sec6x + \tan6x}\cdot(\sec6x\tan6x\cdot 6 + \sec^2\!6x\cdot 6)

    . . . . . . . . . \displaystyle f'(x) \;=\;\frac{6\sec6x\,(\tan6x + \sec6x)}{\sec6x + \tan6x} \;=\;6\sec6x


    \text{Then: }\;f''(x) \;=\;6\sec6x\tan6x\cdot 6 \;=\;36\sec6x\tan6x

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2011
    Posts
    2
    Perfect, thanks for the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of Trig functions/ The secant proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 8th 2011, 12:17 AM
  2. taking the derivative of trig functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 10th 2010, 01:06 PM
  3. Replies: 2
    Last Post: September 24th 2009, 10:43 PM
  4. Derivative with trig functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 7th 2008, 08:14 PM
  5. Derivative with trig functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 6th 2008, 05:26 PM

Search Tags


/mathhelpforum @mathhelpforum