1. Not finding help here? Sign up for a free 30min 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!

Simple Question - Derivative of log(coshx-1)

  1. May 3, 2017 #1
    1. The problem statement, all variables and given/known data
    f(x) = Log(cosh(x-1)), find f'(x).

    2. Relevant equations


    3. The attempt at a solution
    f'(x) = [1/cosh(x) - 1] * d/dx [cosh(x) - 1], => f'(x) = sinh(x) / [cosh(x) - 1]

    Although, my marking scheme says the answer should instead be; cosh(x) + 1 / sinh(x).

    Can someone explain where I'm going wrong? Thanks.
     
  2. jcsd
  3. May 3, 2017 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Check the function f(x) in the problem. Is it really ##f(x)=\log(\cosh(x-1))##?
     
  4. May 3, 2017 #3
    Screenshot (56).png

    Question 16. Definitely yeah.
     
  5. May 3, 2017 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    log(cosh(x)-1) is not the same as log(cosh(x-1)). The argument of cosh is x in the original problem, you wrote(x-1).
    You made errors with the parentheses in the solution. Somehow you wrote the correct derivative, but the marking scheme is not correct.
     
  6. May 3, 2017 #5
    Ah apologies, I tend to overuse brackets & at times make mistakes as a result. I'm working from a University past paper so I assumed the marking scheme to be correct no matter what as it's a paper from 2014.

    So in either circumstances with the parenthesis, there is no way that function could have a derivative equal to the marking schemes answer?
     
  7. May 3, 2017 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The derivative of f(x)=log(cosh(x)-1) is ##\frac{sinh(x)}{\cosh(x)-1}## as you wrote, and that is not among the given answers.
     
  8. May 3, 2017 #7

    Mark44

    Staff: Mentor

    Overuse is not the problem here -- [1/cosh(x) - 1] -- in the righthand side of the first equation above.
    What you wrote means ##\frac 1 {\cosh(x)} - 1##, which I'm sure isn't what you intended.

    When you write a fraction where either the numerator or the denominator contains multiple terms, you have to surround that part with parentheses or other enclosing symbols.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Simple Question - Derivative of log(coshx-1)
Loading...