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Homework Help: Derivative of y = (1/x) + sqrt(cos x)

  1. Nov 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Evaluate the derivative of the function y = (1/x) + sqrt(cos x) at the given point, (pi/2, 2/pi)

    2. Relevant equations

    3. The attempt at a solution
    I used power rule on (1/x) and chain rule on sqrt(cos x) but when I was simplifying, there is a sqrt(cos x) in one of the denominators, which then becomes undefined when I plug in pi/2, so I'm confused what I did wrong, I'm pretty sure I used the correct rules and I'm pretty sure I simplified correctly, so why is it coming out undefined
  2. jcsd
  3. Nov 4, 2015 #2
    Take a look at the domain of the derivative you calculated.
  4. Nov 5, 2015 #3


    Staff: Mentor

    What's more, Michelle, take a look at the domain of ##y = \frac 1 x + \sqrt{\cos x}##. Consider the fact that there are intervals where cos(x) is negative, so its square root isn't real on those intervals.
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