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First, second and third deriative of ln (tan x )

  1. Apr 13, 2014 #1
    1. The problem statement, all variables and given/known data

    y=ln(tan x), dy/dx=2/(sin2x) and d2y/dx2= -4(cos 2x)/(sin 2x)^2 , show that d3y/dx3 = ((4)(3+cos 4x))/(sin 2x)^3 ... i got the solution for dy/dx and d2y/dx2 but not d3y/dx3 , can anyone show me how to get d3y/dx3 please? Thanks in advance!

    2. Relevant equations



    3. The attempt at a solution
    https://www.flickr.com/photos/123101228@N03/13824984513/ (working)
     
  2. jcsd
  3. Apr 13, 2014 #2

    SammyS

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    Here is an image of the photo in your link:

    attachment.php?attachmentid=68637&stc=1&d=1397436503.jpg

    Of course, there are a few ways to express the functions involved.

    You first derivative is correct.

    Why not write ##\displaystyle \ \frac{2}{\sin(2x)}\ ## as ##\displaystyle \ 2\csc(2x) \ ?##

    That's easy to differentiate.

    Then use the product rule for y''' .
     

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