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

[Michele Nunes]

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

 

[Lord Anoobis]

Take a look at the domain of the derivative you calculated.

 

[Mark44]

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.