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

  • #1

Homework Statement


Evaluate the derivative of the function y = (1/x) + sqrt(cos x) at the given point, (pi/2, 2/pi)

Homework Equations




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
 

Answers and Replies

  • #2
130
22
Take a look at the domain of the derivative you calculated.
 
  • #3
35,017
6,767
Take a look at the domain of the derivative you calculated.
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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