Home / AP Calculus BC 3.4 Differentiating Inverse Trigonometric Functions – Exam Style Questions – MCQs

AP Calculus BC 3.4 Differentiating Inverse Trigonometric Functions - Exam Style Questions - MCQs - New Syllabus

AP Calculus BC-MCQs and Answers - All Topics

Question

If \(y=\sin^{-1}(x-1)\), then \(\dfrac{dy}{dx}=\)
A) \( \displaystyle \frac{1}{\sqrt{\,2-x\,}} \)
B) \( \displaystyle \frac{1}{\sqrt{\,1-x^{2}\,}} \)
C) \( \displaystyle \frac{1}{\sqrt{\,2x-x^{2}\,}} \)
D) \( \displaystyle \frac{1}{x^{2}-2x+2} \)
▶️ Answer/Explanation
Detailed solution
\(\dfrac{d}{dx}\big(\sin^{-1}u\big)=\dfrac{u’}{\sqrt{1-u^{2}}}\). Take \(u=x-1\Rightarrow u’=1\).
\(\displaystyle \frac{dy}{dx}=\frac{1}{\sqrt{\,1-(x-1)^{2}\,}}=\frac{1}{\sqrt{\,1-(x^{2}-2x+1)\,}}=\frac{1}{\sqrt{\,2x-x^{2}\,}}\).
✅ Correct: C
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