Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 22

$dy/dx=-\tan(x)$

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 $\frac{1}{cos(x)} \times -sin(x)=-\frac{sin(x)}{cos(x)}=\boxed{-\tan(x)}$.