Home / AP Calculus AB 3.4 Differentiating Inverse Trigonometric Functions – MCQs

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) \(2\)

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