Results 1 to 6 of 6

Math Help - Implicit Differentiation Question

  1. #1
    Senior Member
    Joined
    Jul 2008
    Posts
    347

    Exclamation Implicit Differentiation Question

    Hi

    Could someone please show me how to differentiate y = [ln(x)]^(sinx)?

    Thanxx a lot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    ynj
    ynj is offline
    Senior Member
    Joined
    Jul 2009
    Posts
    254
    (\ln x)^{\sin x}=e^{\ln \ln x\sin x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    y = ln(x)^(sin(x))

    ln(y) = sin(x)ln(ln(x))

    1/y dy/dx = cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x

    dy/dx = y[cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x]

    dy/dx = ln(x)^(sin(x))[cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2008
    Posts
    347

    Exclamation

    Quote Originally Posted by Calculus26 View Post
    y = ln(x)^(sin(x))

    ln(y) = sin(x)ln(ln(x))

    1/y dy/dx = cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x

    dy/dx = y[cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x]

    dy/dx = ln(x)^(sin(x))[cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x]
    Can that part be simplified to:

    sin(x) / (x ln(x))
    = 1 / ln(x)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    How do you get sin(x)/[xln(x)] simplifying to 1/ln(x) ?

    you are not suggesting sin(x)/x =1 are you?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,306
    Thanks
    1282
    Quote Originally Posted by xwrathbringerx View Post
    Can that part be simplified to:

    sin(x) / (x ln(x))
    = 1 / ln(x)
    \lim_{x\rightarrow 0} \frac{sin(x)}{x}= 1 but, in general, \frac{sin(x)}{x}\ne 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on implicit differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2010, 03:38 PM
  2. Implicit Differentiation question
    Posted in the Calculus Forum
    Replies: 11
    Last Post: February 12th 2010, 02:18 AM
  3. another implicit differentiation question
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 6th 2010, 03:43 PM
  4. Implicit Differentiation Question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 7th 2008, 06:08 AM
  5. Question about Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 23rd 2007, 09:34 PM

Search Tags


/mathhelpforum @mathhelpforum