Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises - Page 169: 32

\[\frac{{dy}}{{dx}} = {\sec ^2}x - {\csc ^2}x\]

\[\begin{gathered} y = \tan x + \cot x \hfill \\ \hfill \\ differentiate \hfill \\ \hfill \\ \frac{d}{{dx}} = \frac{d}{{dx}}\,\,\left[ {\tan x} \right] + \frac{d}{{dx}}\,\,\left[ {\cot x} \right] \hfill \\ \hfill \\ then \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = {\sec ^2}x - {\csc ^2}x \hfill \\ \end{gathered} \]