Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivatives of natural logarithmic functions

  1. Sep 8, 2008 #1
    f(x) = ln (12x-5/9x-2)

    f'(x) = (4/3) (1/ln10)(9x-2/12x-5)

    Is this correct??
     
  2. jcsd
  3. Sep 8, 2008 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Instead of ln(10) you should put ln(base of the logarithm), in this case; ln(e) = 1. When deriving log(x) (base 10), you can rewrite to ln(x)/ln(10). ln(10) is just a constant, so the derivative of this is 1/ln(10) * 1/x.

    Also, I think you didn't do the chain rule quite right.
     
  4. Sep 8, 2008 #3
    Then, is this
    f(x) = ln (12x-5)
    g(x) = ln (9x-2)
    f'(x) = 12/12x-5
    g'(x) = 9/9x-2

    Correct??
     
  5. Sep 8, 2008 #4
    Is this correct:

    (12/12(ln9x-2)-5)-(9/9x-2)
     
    Last edited: Sep 8, 2008
  6. Sep 8, 2008 #5

    Defennder

    User Avatar
    Homework Helper

    This should not have ln inside. What is d/dx ln(12x-5) ? You've got it from above, just put it into this one.
     
  7. Sep 9, 2008 #6

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    I have the feeling you are guessing more than working systematically. Actually there are two ways to solve this. One is by using the chain rule:
    set y = (12x - 5) / (9x - 2). Then the derivative of ln(y) is 1/y . dy/dx.

    The other way is to first use ln(a/b) = ln(a) - ln(b) and then use the sum rule to differentiate (you still need the chain rule!).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?