Results 1 to 2 of 2

Math Help - Derivative of nested trigonometric functions

  1. #1
    Senior Member vaironxxrd's Avatar
    Joined
    Nov 2010
    From
    USA
    Posts
    428
    Thanks
    1
    Awards
    1

    Derivative of nested trigonometric functions

    Hello Everyone,

    Today I got stuck on a group of similar problems and wanted to present an example of one.

    I have have the following problem Dx[sin^2(sin \pi \theta)]

    The way I solve it is the following:

    Using the chain rule over and over again...

    2u * \frac{d}{d _\theta} u
    u = sin(sin \pi \theta)

    2[sin(sin \pi \theta)] \frac{d}{d _\theta} sin(sin \pi \theta)

    2[sin(sin \pi \theta)] cos( sin \pi \theta) \frac{d}{d _\theta} sin(\pi \theta)

    2[sin(sin \pi \theta)] cos( sin \pi \theta) cos(\pi \theta) \frac{d}{d _\theta} (\pi\theta)

    = 2[sin(sin \pi \theta)] cos( sin \pi \theta) cos(\pi \theta) (\pi)

    Wolframalpha tells me the answer is: \pi sin(2sin\pi\theta)cos(\pi\theta)

    Did I not simplify correctly? Din't use the product rule at some point?
    I'm still a bit confused of which rules to use.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49

    Re: Derivative of nested trigonometric functions

    No worries, just simplify using a trig identity
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] derivative of rational/trigonometric functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 25th 2011, 08:11 PM
  2. Replies: 1
    Last Post: November 7th 2010, 03:37 PM
  3. Replies: 8
    Last Post: September 13th 2009, 04:34 AM
  4. Replies: 4
    Last Post: November 3rd 2008, 07:09 PM
  5. Derivative of trigonometric functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 4th 2008, 07:11 PM

Search Tags


/mathhelpforum @mathhelpforum