1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Am I right?

  1. Dec 3, 2005 #1
    Ok, I worked this derivative problem, but my book has a different answer than what I got. I'm not sure why.

    I need to compute the derivative of log base3 of (x^3 + 2x)

    I came out with:

    1/((x^3 + 2x)ln3)

    The book says that the answer is the same as mine except the numerator has a (3x^2 + 2) in it.

    Why would you put the derivative of the x value of the log function in the numerator.

    My book says that D log base a of x = 1/xlna

  2. jcsd
  3. Dec 3, 2005 #2


    User Avatar
    Gold Member

    The book is right. Don't forget the chain rule. It is true that
    , but
  4. Dec 3, 2005 #3


    User Avatar
    Science Advisor

    Have you heard of the "chain rule"?
    The derivative of log3{x^3 + 2x}[/sub] is
    [tex]\frac{1}{x^2+2x}(3x^2+ 2}[/tex].
  5. Dec 3, 2005 #4
    Your mistake was to proceed with the wrong inverse function

    [tex]\log_{3} x^{3} + 2x [/tex]

    [tex]x^{3} + 2x = 3^{y} [/tex]

    From this point you had to isolate x then differentiate the function and put it to power -1, which is not efficient. Use the chain rule http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/proofs/chainruleproof.html" [Broken]
    Last edited by a moderator: May 2, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook