AP Calculus AB: 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions – Exam Style questions with Answer- FRQ

Concept: The limit expression represents the definition of the derivative of \( \sec x \) at \( x = \frac{\pi}{3} \). Step 1: Recall the derivative of secant: \[ \frac{d}{dx} \sec x = \sec x \tan x \] Step 2: Evaluate at \( x = \frac{\pi}{3} \): \[ f’\left(\frac{\pi}{3}\right) = \sec\left(\frac{\pi}{3}\right) \tan\left(\frac{\pi}{3}\right) \] Numerical values: \[ \sec\left(\frac{\pi}{3}\right) = 2 \] \[ \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \] \[ f’\left(\frac{\pi}{3}\right) = 2\sqrt{3} \]