Results 1 to 6 of 6

Math Help - natural differentiation

  1. #1
    Junior Member
    Joined
    Nov 2010
    Posts
    57

    natural differentiation

    y= e^sin 2x

    Solution attempt:

    lny = sin 2x

    lny = 2sinxcosx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2009
    Posts
    226
    \dfrac{d}{dx}\left[e^u\right] = e^u \times \dfrac{du}{dx}

    For y = e^{\sin(2x)}, let u = \sin(2x). Then, \dfrac{du}{dx} = 2\cos(2x).

    Now, it is only a matter of substituting the values of u and \dfrac{du}{dx} into the first equation at the top.

    y' = e^{\sin(2x)} \times 2\cos(2x) = 2e^{\sin(2x)}\cos(2x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member integral's Avatar
    Joined
    Dec 2009
    From
    Arkansas
    Posts
    200
    y= e^{sin 2x}

    \ln(y)=\sin(2x)

    \frac{dy}{ydx}=\frac{d}{dx}\left [ \sin(2x) \right ] implicite differentiation.

    \frac{dy}{ydx}=2\cos(2x)chain rule

    \frac{dy}{dx}=2y\cos(2x)

    y=e^{sin 2x}

    \frac{dy}{dx}=2e^{sin 2x}\cos(2x)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2010
    Posts
    57
    Then, \dfrac{du}{dx} = 2\cos(2x).

    Both of you have the correct answer, I get the use of the chain rule and it looks very clean but could you also use the product rule for \dfrac{du}{dx}?

    Thus making \dfrac{du}{dx}=2\sin+2x\cos

    did I just make a mistake?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member integral's Avatar
    Joined
    Dec 2009
    From
    Arkansas
    Posts
    200
    Product rule applies when you have the form: f(x)=p(x)q(x). (which you don't have here)

    I am not sure where you are geting 2sin(2x)+2cos(2x) but if you will notice, the form of f(x) needing to use the chain rule is: f(x)=p(q(x))

    where p(x)=sin(x) and q(x)=2x
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Nov 2010
    Posts
    57
    Thank you integral, was confused as to which was the inside/ outside function. In fact I am rather ignorant of the transcendental functions altogether as I looked at sin2x as the product of sin and 2x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 28th 2011, 10:16 AM
  2. Natural Log Differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2010, 09:17 PM
  3. Implicit natural log differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 17th 2010, 09:28 PM
  4. Implicit Differentiation w/ Natural Log
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 22nd 2009, 09:22 AM
  5. Natural log differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 26th 2009, 12:33 PM

Search Tags


/mathhelpforum @mathhelpforum