Results 1 to 2 of 2

Math Help - differentiate

  1. #1
    Junior Member
    Joined
    Apr 2011
    Posts
    29

    differentiate

    Hi there!

    Can someone please explain to me the reason for,

    y = In[In(sin x)]

    does it exist?
    and the answer cannot be
    dy/dx = cot x / In (sin x) because it is apparently it is incorrect.

    would the anwer be: dy/dx = In (sin x) / In (sin x)
    but if it is, it does not make sense when using the formula of,
    d/dx (In f(x)) = f ' (x) / f (x )

    So, would the answer then be, -1 < sin x < 1
    or is the answer, 0 < sin x < 1

    and also with y = In[In(cos x)]
    does not exist due to (In cos x) always being negative.

    Thanks heaps if you get this, true champ!!!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    FYI the natural log is written as ln(x) - that's a lower case L.

    Looking at the domain of the original equation it would appear that no values satisfy the equation since the argument must be positive.

    The range of sin(x) is -1 \leq \sin(x) \leq 1. We can immediately discard the negative values (and 0) of sin(x) to satisfy the inner bracket. For 0 \leq x \leq 1 then \ln(x) \leq 0 and as mentioned above the argument of a log must be positive so all values of x lie outside the domain of y.

    It would then follow that if the original function cannot be satisfied then there must be no derivative

    Hope this makes sense and for what it's worth I get the same value for the derivative as you: \dfrac{dy}{dx} = \dfrac{cot(x)}{\ln(\sin(x))}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differentiate tan^3[2x]
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 15th 2010, 05:07 AM
  2. Differentiate 1 / (t+3e^t)
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 11th 2010, 11:40 PM
  3. differentiate
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 9th 2009, 12:22 PM
  4. How do you differentiate e^xy?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 28th 2009, 09:57 AM
  5. differentiate y=a(1-exp^-bx)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 10th 2008, 04:09 AM

Search Tags


/mathhelpforum @mathhelpforum