Results 1 to 5 of 5

Math Help - Differentiating a exponential function.

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    16

    Differentiating a exponential function.

    Differentiate (w.r.t x ) e^{2logx + 3x}

    I tried to solve it as follows:-

    e^{2logx} + e^{3x}


     \frac{\mbox{d}}{\mbox{dx}}(e^{2logx}) +  \frac{\mbox{d}}{\mbox{dx}}(e^{3x})

    Using chain rule my answer is:-

    e^{2logx}. \frac{\ 2}{x} + e^{3x}.3

    Is it correct.? The actual answer is different.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by vivek_master146 View Post
    Is it correct.? The actual answer is different.

    You can simplify:

    e^{2\log x}=e^{\log x^2}=x^2 .

    and your function is:

    f(x)=x^2e^{3x}

    not

    f(x)=x^2+e^{3x}


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    16
    Quote Originally Posted by FernandoRevilla View Post
    You can simplify:

    e^{2\log x}=e^{\log x^2}=x^2 .

    and your function is:

    f(x)=x^2e^{3x}

    not

    f(x)=x^2+e^{3x}
    Thanks for reply. The first line totally went over my head. How did you derive x^2.

    One more thing:- e^{a +b} = e^a + e^b \ OR \  e^a.e^b

    Sorry for simple questions. I am directly studying graduation level maths without studying higher secondary maths.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by vivek_master146 View Post
    Thanks for reply. The first line totally went over my head. How did you derive x^2.

    By definition of natural logarithm: e^{\log A}=A


    One more thing:- e^{a +b} = e^a + e^b \ OR \  e^a.e^b

    The second one.


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,453
    Thanks
    1868
    You really should learn the "laws of exponents" better before attempting calculus.

    e^{a+ b}= e^ae^b, not e^a+ e^b,
    (e^a)^b= e^{ab},
    and, since e^x and ln(x) are "inverse" functions,
    e^{ln(x)}= x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differentiating exponential functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 1st 2010, 05:46 PM
  2. Differentiating an exponential function..
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 3rd 2010, 09:26 PM
  3. Replies: 4
    Last Post: May 2nd 2010, 07:42 AM
  4. differentiating exponential functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 26th 2009, 04:29 PM
  5. Replies: 2
    Last Post: January 27th 2007, 07:53 AM

Search Tags


/mathhelpforum @mathhelpforum