Results 1 to 3 of 3

Math Help - differentiation

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    33

    Arrow differentiation

    why does the power rule for differentiation doesn't apply to a function like y = x^(cosx)?

    how do you solve y = x^(cosx)

    hmm...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2008
    Posts
    792
    Because the power rule is proved for constant exponents. To differentiate something like, x^(cos(x)), simply use the inverse property of logarithms:
    e^{\ln{x}} = x

    y = x^{\cos{x}} = e^{\ln{x^{\cos{x}}}} = e^{\cos{x}\ln{x}}

    Use chain rule to differentiate.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Another way to use the same idea is if you have y=x^{\cos(x)}, then just take the natural log of both sides and use the fact that \frac{d}{dx} \ln(y) = \frac{y'}{y} if y is a function of x. You can say in general I think that y' = y*\frac{d}{dx} \left( \ln(f[x]) \right) (there's some conditions on that of course). That's the way I liked doing this problems.
    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