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Double check a Calculus problem

  1. Sep 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Differentiate with respect to the variable
    y=cos^-1((x/4)

    2. Relevant equations
    cos^-1 x/a
    inverse cosine function
    -1/root a^2-x^2
    3. The attempt at a solution
    Differentiated
    dy/dx=(1/root4^2-x^2)/3

    Brought in the 3 for
    dy/dx=0.3x(1/root4^2-x^2)

    at this point i cant really see how to simplify this further.

    Can it be done. are the current steps correct?
     
  2. jcsd
  3. Sep 15, 2015 #2

    RUber

    User Avatar
    Homework Helper

    What you have written is difficult to read. Please use latex, and if nothing else, use parentheses.
    You start with:
    ## \cos^{-1} \frac{x}{a} = -\frac{1}{\sqrt{a^2 - x^2}}. ##
    In the problem you are given, a = 4.
    You should be able to take the derivative using the chain rule for ## - (a^2 - x^2)^{-1/2}##.
    I have no clue where your 3 or .3 came from.
     
  4. Sep 15, 2015 #3

    Mark44

    Staff: Mentor

    Problems with derivatives belong in the Calculus section, not in the Precalc section.
    The above is the formula for the derivative of the inverse cosine.

    Also, you need parentheses to indicate what's in the radical -- -1/root (a^2-x^2)
    Where did the 3 come from? And what happened to the minus sign?
     
    Last edited: Sep 15, 2015
  5. Sep 15, 2015 #4
    I've unintentionally left out part of the question. Reworked...

    1. The problem statement, all variables and given/known data
    Differentiate with respect to the variable
    y= (1/3) cos^-1 ((x/4)

    2. Relevant equations
    cos^-1 (x/a)
    inverse cosine function
    -1/root(a^2-x^2)
    3. The attempt at a solution
    Differentiated
    dy/dx=(1/root(4^2-x^2))/3

    Could you comment on whether now this clears up you queries.

    Thanks
     
  6. Sep 15, 2015 #5

    Mark44

    Staff: Mentor

    Better: d/dx(cos-1(x/a)) = -1/√(a2 - x^2)
    Where did your minus sign go?
     
  7. Sep 15, 2015 #6
    I was under the impression that the -1 goes because of the (1/3)
     
  8. Sep 15, 2015 #7

    Mark44

    Staff: Mentor

    No. I don't know why you would think that.
     
  9. Sep 15, 2015 #8
    I assume i am totally wrong in that case
     
  10. Sep 15, 2015 #9

    Mark44

    Staff: Mentor

    d/dx[(1/3) cos-1 ((x/4)] = (1/3) * d/dx[cos-1 ((x/4)] (derivative of a constant multiple rule for differentiation)
    = (1/3) * ?
     
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