Results 1 to 4 of 4

Math Help - Indice differentiation

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    145

    Indice differentiation

    Given
    f(x,y)=x^{xy}

    How do we evaluate:
    {{\partial f} \over {\partial x}}
    and
    {{\partial f} \over {\partial y}}

    I generated the answer with mathematica and the answers seem different from a textbook.
    Thanks
    Last edited by chopet; December 5th 2007 at 02:16 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276

    Clarification?

    chopet, what do you mean by the comma in the exponent?

    --Kevin C.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2007
    Posts
    145
    no comma, sorry. Plain xy to be differentiated.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,846
    Thanks
    321
    Awards
    1
    Quote Originally Posted by chopet View Post
    Given
    f(x,y)=x^{xy}

    How do we evaluate:
    {{\partial f} \over {\partial x}}
    and
    {{\partial f} \over {\partial y}}

    I generated the answer with mathematica and the answers seem different from a textbook.
    Thanks
    f(x,y) = x^{xy} = \left ( x^x \right ) ^y

    So
    \frac{\partial f}{\partial x} = y \left ( x^x \right )^{y - 1} \cdot (ln(x) + 1) \cdot x^x
    by the chain rule so
    \frac{\partial f}{\partial x} = y(ln(x) + 1) \left ( x^x \right )^y

    Since x is a constant with respect to the y derivative:
    \frac{\partial f}{\partial y} = ln \left ( x^x \right ) \cdot \left ( x^x \right ) ^y

    \frac{\partial f}{\partial y} = x \cdot ln(x) \cdot \left ( x^x \right ) ^y

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. indice
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 9th 2010, 09:23 PM
  2. indice thing 1
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 10th 2010, 07:25 AM
  3. indice thing 2
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 10th 2010, 01:42 AM
  4. indice thing
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 22nd 2009, 09:28 AM
  5. simplify indice
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 21st 2008, 11:58 AM

Search Tags


/mathhelpforum @mathhelpforum