Results 1 to 2 of 2

Math Help - Differentiation

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    132

    Differentiation

    Hello!

    How do I differentiate x ^ (sin x)??

    Thank you for helping!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,751
    Thanks
    651
    Hello, Tangera!

    How do I differentiate: . y \:=\: x^{\sin x} ?
    Take logs: . \ln y \:=\:\ln\left(x^{\sin x}\right) \quad\Rightarrow\quad \ln y \:=\:\sin x\!\cdot\!\ln x

    Differentiate implicitly: . \frac{1}{y}\!\cdot\!\frac{dy}{dx}\;=\;\sin x\!\cdot\!\frac{1}{x} + \cos x\!\cdot\!\ln x

    Then: . \frac{dy}{dx}\;=\;y\left(\frac{\sin x}{x} + \cos x\!\cdot\!\ln x\right)


    Therefore: . \frac{dy}{dx}\;=\;x^{\sin x}\left(\frac{\sin x}{x} + \cos x\!\cdot\!\ln x\right)

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  2. Differentiation and partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2010, 10:16 PM
  3. Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 4th 2010, 10:45 AM
  4. Differentiation Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 25th 2010, 06:20 PM
  5. Differentiation and Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 6th 2009, 04:07 AM

Search Tags


/mathhelpforum @mathhelpforum