Results 1 to 7 of 7

Math Help - derivitive of e to the x root

  1. #1
    Member
    Joined
    Jul 2008
    Posts
    128
    Awards
    1

    derivitive of e to the x root

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294
    Are you asking "How do you find the derivative of \displaystyle y = \sin{\left(e^{3x}\right)}"?

    If so, use the Chain Rule.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2008
    Posts
    128
    Awards
    1
    Quote Originally Posted by Prove It View Post
    Are you asking "How do you find the derivative of \displaystyle y = \sin{\left(e^{3x}\right)}"?

    If so, use the Chain Rule.
    Yes, I know how to use chain rule for examples like below:


    (3x +2){4}

    However, I'm unsure how to apply it to the one I showed at start of thread.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294
    Let \displaystyle u = e^{3x} so that \displaystyle y = \sin{u}.

    You should know that \displaystyle \frac{dy}{dx} = \frac{du}{dx}\,\frac{dy}{du}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jul 2008
    Posts
    128
    Awards
    1
    Quote Originally Posted by Prove It View Post
    Let \displaystyle u = e^{3x} so that \displaystyle y = \sin{u}.

    You should know that \displaystyle \frac{dy}{dx} = \frac{du}{dx}\,\frac{dy}{du}.
     derivative  of \displaystyle u = e^{3x} and X by \displaystyle y = \sin{u}

    im lost if anyone could show the steps i that would be great
    Last edited by realistic; April 1st 2011 at 07:28 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Just in case a picture helps...

    Given so many layers...



    ... we need to apply...



    ... the chain rule at least twice. (Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Probably best to think of it like...



    ... then zoom in (mentally at least) on the question of differentiating e to the 3x...



    ... and use the bottom row to fill the blank in the previous. But if you want to put both in one picture... well, scientists here at the Laboratoire Ballon have struggled to come up with...



    ... but improvements gratefully received.

    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,423
    Thanks
    1332
    y= sin(e^{3x})
    Let v= 3x and u= e^v so y= sin(u)

    The derivative of y= sin(u) with respect to u is cos(u).

    The derivative of u= e^v with respect to v is e^v.

    The derivative of v= 3x with respect to x is 3.

    Now put them all together- by the chain rule,
    \frac{dy}{dx}= \frac{dy}{du}\frac{du}{dv}\frac{dv}{dx}

    With practice, you can learn to do those without having to write out the substitituions:

    "The derivative of sine is cosine so the derivative of cos(e^{3x}) is sin(e^{3x}) times the dervative of e^{3x} which is e^{3x} times the derivative of 3x, which is 3"
    Last edited by HallsofIvy; April 2nd 2011 at 09:16 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. derivitive
    Posted in the Calculus Forum
    Replies: 14
    Last Post: November 17th 2009, 07:27 PM
  2. derivitive help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 1st 2009, 11:47 AM
  3. Derivitive
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 11th 2008, 05:39 PM
  4. Need Derivitive Help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2007, 03:09 PM
  5. second derivitive ..HELP!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 29th 2007, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum