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

1. Nov 4, 2015

### Michele Nunes

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. Nov 4, 2015

### Lord Anoobis

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

3. Nov 5, 2015

### 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.