Results 1 to 10 of 10

Math Help - Differentiation of exponential

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    5

    Differentiation of exponential

    Hey, I'm reviewing calculus (its been sometime since I took it) and I'm trying to do some examples from the book but I'm pretty sure I'm doing it wrong.
    Heres the first one:


    Attached Thumbnails Attached Thumbnails Differentiation of exponential-ex1.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Agent View Post
    Hey, I'm reviewing calculus (its been sometime since I took it) and I'm trying to do some examples from the book but I'm pretty sure I'm doing it wrong.
    Heres the first one:


    you either have to use the chain rule here, or distribute the power and use the product rule.

    you seem to be attempting the chain rule. so i will ask you this, what is the derivative of te^{-2t}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    5
    The exponential confuses me but I think its,

    <br />
te^{-2t} * -2<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Agent View Post
    The exponential confuses me but I think its,

    <br />
te^{-2t} * -2<br />
    well, it's not. you have a product of functions here, you need to use the product rule: \frac d{dx} [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2008
    Posts
    5
    so can we say, f(x) = te and g(x) = -2t?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Agent View Post
    so can we say, f(x) = te and g(x) = -2t?
    no. f(t) = t is one function, g(t) = e^{-2t} is the other.

    making -2t as one function makes no sense, right? since you are saying there is some power without a base just floating around magically
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2008
    Posts
    5
    ok so if I'm following correctly,

    te^{-2t}

    te^{-2t} * 2 + 1 * e^{-2t}
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Agent View Post
    ok so if I'm following correctly,

    te^{-2t}

    te^{-2t} * 2 + 1 * e^{-2t}
    almost. the derivative of e^{-2t} is -2e^{-2t}. with that said,

    \frac d{dt}\bigg( t e^{-2t}\bigg) = -2te^{-2t} + e^{-2t} = e^{-2t}(1 - 2t)

    now, can you do the original problem?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2008
    Posts
    5
    Quote Originally Posted by Jhevon View Post
    almost. the derivative of e^{-2t} is -2e^{-2t}. with that said,

    \frac d{dt}\bigg( t e^{-2t}\bigg) = -2te^{-2t} + e^{-2t} = e^{-2t}(1 - 2t)

    now, can you do the original problem?
    Awesome. I got it now. Thank You
    Follow Math Help Forum on Facebook and Google+

  10. #10
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Agent View Post
    Awesome. I got it now. Thank You
    do you have the answer in the back of your text or something? if not, you mind posting your solution?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exponential differentiation.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 11th 2010, 09:02 AM
  2. Exponential Differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 1st 2009, 01:40 PM
  3. exponential differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 12th 2009, 04:30 PM
  4. exponential differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 12th 2009, 02:52 AM
  5. exponential differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 3rd 2007, 10:19 AM

Search Tags


/mathhelpforum @mathhelpforum