AP Calculus AB 3.4 Differentiating Inverse Trigonometric Functions - MCQs - Exam Style Questions
No-Calc Question
If \(f(x)=\sin^{-1}x\), then \(f’\!\left(\dfrac{\sqrt{3}}{2}\right)=\) ?
(A) \(\dfrac{\pi}{6}\)
(B) \(\dfrac{\pi}{3}\)
(C) \(\dfrac{4}{7}\)
(D) \(2\)
▶️ Answer/Explanation
\(f'(x)=\dfrac{1}{\sqrt{1-x^{2}}}\).
\(f’\!\left(\dfrac{\sqrt{3}}{2}\right)=\dfrac{1}{\sqrt{1-\frac{3}{4}}}=\dfrac{1}{\sqrt{\frac{1}{4}}}=2\).
✅ Answer: (D) \(2\)