Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Calculus and Exponents

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    New Zealand
    Posts
    35

    Calculus and Exponents

    A question says to find the derivative of

    e^3/(sin(x)+1)

    The answer I got was -e^3cosx/(sinx+1)^2

    My friend got
    (e^3sinx+e^3 - e^3cosx)/(sinx+1)^2

    The online calculators all agree with me, but he used the quotient rule (so did I), but I pulled e^3 out of it and used 1/sinx+1 to perform the quotient rule.

    Which is the correct method?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602

    Re: Calculus and Exponents

    I'd write it as \displaystyle \begin{align*} y = e^3 \left[ \sin{(x)} + 1 \right] ^{-1} \end{align*} then let \displaystyle \begin{align*} u = \sin{(x)} + 1 \implies y = e^3 \, u^{-1} \end{align*}. Then \displaystyle \begin{align*} \frac{du}{dx} = \cos{(x)} \end{align*} and \displaystyle \begin{align*} \frac{dy}{du} = -e^3 \, u^{-2} = -e^3 \left[ \sin{(x)} + 1 \right] ^{-2} \end{align*}. So \displaystyle \begin{align*} \frac{dy}{dx} = -e^3 \cos{(x)} \left[ \sin{(x)} + 1 \right] ^{-2} = -\frac{ e^3 \cos{(x)} }{ \left[ \sin{(x)} + 1 \right] ^2} \end{align*}. Your answer is correct.
    Thanks from MarkFL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Calculus and Exponents

    Your friend failed to realize that e^3 is a constant, and so its derivative is zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: June 25th 2010, 11:41 PM
  2. calculus with exponents
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 22nd 2010, 04:42 PM
  3. Replies: 1
    Last Post: February 11th 2010, 08:09 AM
  4. Replies: 1
    Last Post: June 23rd 2008, 10:17 AM
  5. Exponents and Logarithms Calculus questions.
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 28th 2007, 09:33 PM

Search Tags


/mathhelpforum @mathhelpforum