if $f(x)=\tan(3x)$, then $f'(\pi/9)=$? I thought the answer was $4$ but my teacher marked it wrong. Work: $f'(x) = \sec^2(3x)\cdot 3 = \frac 3{\cos^2(3x)} = \frac{3}{\cos^2(\pi/3)} = 3/(3/4) = 4$.
2026-04-02 17:36:42.1775151402
Derivative of Trig. Function
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It's almost right, but $\cos \frac{\pi} 3=\frac 1 2$, not $\sqrt{3}\over 2$.
Thus the answer is
$$\frac{3}{\cos^2(\pi/3)} = 3/(1/4) =12$$