Results 1 to 4 of 4

Math Help - Differentiation and Chain Rule

  1. #1
    Junior Member madmax29's Avatar
    Joined
    Feb 2009
    Posts
    33

    Differentiation and Chain Rule

    Question: y=3Sin^4(2x)

    ...how do you solve this using the chain rule;

    dy/dx= dy/du X du/dx,

    y =3Sin^4 where u = 2x <<<< is this correct?

    what do i do after this, can someone explain

    i think im using differentiation rules;
    sin x = cos x
    x^n = nx ^n-1
    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
    Yes, although you need to use the chain rule three times because of the sin function

    Set u = 2x and v = sin(u) so that y=3v^4


    By the chain rule: \dfrac{dy}{dx} = \dfrac{dy}{dv} \cdot \dfrac{dv}{du} \cdot \dfrac{du}{dx}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member madmax29's Avatar
    Joined
    Feb 2009
    Posts
    33
    therefore

    dy/du= nx^n-1 >>> = 3v^4

    du/dv= 2x >>> =2

    dv/dx= sin (u) >>> cos(u)

    therefore

    \dfrac{dy}{dx} = \dfrac{dy}{dv} \cdot \dfrac{dv}{du} \cdot \dfrac{du}{dx}

    = 3v^3 X Cos (u) X 2

    = 2 Cos (2x) 3 Sin^3 (2x)
    is this correct????
    Follow Math Help Forum on Facebook and Google+

  4. #4
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    No, I don't know where your 3 has gone?

    Your individual differentation is fine, apart from dy/dv which is 12v^3 (you didn't multiply by that 4)

    12v^3 \cdot \cos(u) \cdot 2 = 24v^3\, \cos(u)

    When we put in our original substitutions back we get:

    24\sin^3(u) \cdot \cos(u) = 24\sin^3(2x)\cos(2x)
    Last edited by e^(i*pi); November 7th 2010 at 04:06 AM. Reason: forgot the cubic power on sin(x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] differentiation of e using chain rule
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 25th 2010, 11:34 AM
  2. Chain Rule Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 26th 2010, 01:03 PM
  3. chain rule + differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 25th 2010, 01:16 PM
  4. chain rule differentiation check!
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 8th 2008, 01:08 AM
  5. differentiation - chain rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 9th 2008, 06:14 AM

Search Tags


/mathhelpforum @mathhelpforum