Results 1 to 2 of 2

Math Help - logarithmic differentiation

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    26

    logarithmic differentiation

    Use logarithmic differentiation to find the derivative of the following equation.
    y = (ln(x))^(cos(15 x))

    in the home work i was doing it was a multiple choice question, and i ended up getting it right, but i'm not exactly sure how to get from the question to the answer

    y'= ln(x)^{cos(15x)}(cos(15x)/x(ln(x))-15(sin(15x))(ln(ln(x)))

    i worked out the problem and got everything in this answer except for the (cos(15x)/x(ln(x)) part, and i don't know where it came from in the derivative formulas that i have.

    I'm asking in case there is a question like this on the test and i'll have no idea how to do it correctly.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    y = \ln x^{\cos 15x}

    here's a useful little trick:


    \ln y = \ln \left( {\ln x} \right)^{\cos 15x}  = \cos 15x\ln \ln x<br />

    now differentiate the equation:


    \begin{gathered}<br />
  \frac{{y'}}<br />
{y} = \ln \ln x\frac{d}<br />
{{dx}}\cos 15x + \cos 15x\frac{d}<br />
{{dx}}\ln \ln x \hfill \\<br />
   \hfill \\<br />
   \Leftrightarrow y' = \ln v^{\cos 15x} \left( {\cos 15x\frac{1}<br />
{{x\ln x}} - 15\sin 15x\ln \ln x} \right) \hfill \\ <br />
\end{gathered} <br />
    Last edited by Peritus; February 26th 2008 at 10:33 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logarithmic Differentiation
    Posted in the Calculus Forum
    Replies: 11
    Last Post: February 22nd 2011, 04:58 PM
  2. logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 13th 2010, 01:36 PM
  3. Logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 18
    Last Post: January 2nd 2010, 10:50 PM
  4. logarithmic differentiation to
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 23rd 2009, 06:52 AM
  5. Logarithmic Differentiation Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 26th 2007, 01:58 AM

Search Tags


/mathhelpforum @mathhelpforum