Results 1 to 4 of 4

Math Help - Another Derivative

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    150

    Another Derivative

    Hello All,

    Here is the problem:

    y=\sqrt[n]{\frac{1}{x^m}}

    Here is what I got:
    \frac{dy}{dx}=\frac{-mx}{n}^\frac{-m-n}{n}

    Here is what the answer I was given:
    \frac{dy}{dx}=\frac{-mx}{n}^\frac{-m+n}{n}

    I don't understand how the exponent could be -m+n??? When you take the derivative of a power, you are supposed to subtract one, correct? If so, doesn't
    \frac{-m}{n} -1 = \frac{-m-n}{n}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,401
    Thanks
    1327
    Yes, your answer is the correct one.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    Posts
    150
    Quote Originally Posted by HallsofIvy View Post
    Yes, your answer is the correct one.
    Thats what I thought. I asked just in case I was missing something or overlooking an algebra error.

    Thanks.

    -db
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,685
    Thanks
    616
    Hello, dbakeg00!

    Differentiate: . y\;=\;\sqrt[n]{\frac{1}{x^m}} \;=\;x^{-\frac{m}{n}}


    Here is what I got: . \frac{dy}{dx}\;=\;-\tfrac{m}{n}x^{-\frac{m}{n}-1} \;=\;-\tfrac{m}{n}x^{\frac{-m-n}{n}} . . . . Right!


    Here is what I was given: . \frac{dy}{dx}\;=\;-\tfrac{m}{n}x^{\frac{-m{\color{red}+}n}{n}} . . . . Wrong!

    "They" must have a typo.

    Your work is correct!

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 02:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 11:40 AM
  3. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 06:33 AM
  4. Derivative of arctan in a partial derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 12th 2010, 01:52 PM
  5. Replies: 2
    Last Post: November 6th 2009, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum