Calculus, 10th Edition (Anton)

$dy/dx=-\tan(x)$
Using the chain rule for derivatives, the derivative of a composition of functions $f(g(x))$ is equal to $f'(g(x)) \times g'(x)$. Using this technique leaves $\frac{1}{cos(x)} \times -sin(x)=-\frac{sin(x)}{cos(x)}=\boxed{-\tan(x)}$.