Theorem 2.8.5 Derivatives of trigonometric functions
The derivatives of \(\sin x\) and \(\cos x\) are
\begin{align*}
\diff{}{x} \sin x &= \cos x & \diff{}{x} \cos x &= - \sin x
\end{align*}
Consequently the derivatives of the other trigonometric functions are
\begin{align*}
\diff{}{x} \tan x &= \sec^2 x &
\diff{}{x} \cot x &= -\csc^2 x\\
\diff{}{x} \csc x &= -\csc x \cot x &
\diff{}{x} \sec x &= \sec x \tan x
\end{align*}