Exponential and trigonometric functions practice question 4

Which derivatives do $\tan x$ and $\sec x$ have? Get those right first, then think about the exact values of $\sin$ and $\cos$ at $\dfrac{\pi}{6}$.

$\dfrac{d}{dx}\tan x = \sec^{2}x$ and $\dfrac{d}{dx}\sec x = \sec x\tan x$.

At $\dfrac{\pi}{6}$, $\cos x = \dfrac{\sqrt{3}}{2}$ and $\sin x = \dfrac{1}{2}$, so $\sec x = \dfrac{2}{\sqrt{3}}$ and $\tan x = \dfrac{1}{\sqrt{3}}$.