MHT CET · Maths · Differentiation
\(\frac{d}{d x}\left(\sin ^{-1}\left(3 x-4 x^3\right)\right), \frac{1}{2} < x < 1\) is
- A \(\frac{1}{3 \sqrt{1-x^2}}\)
- B \(\frac{-3}{\sqrt{1-x^2}}\)
- C \(\frac{-1}{3 \sqrt{1-x^2}}\)
- D \(\frac{3}{\sqrt{1-x^2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{-3}{\sqrt{1-x^2}}\)
Step-by-step Solution
Detailed explanation
Let \( x = \sin\theta \). Given \( \frac{1}{2} < x < 1 \implies \sin\left(\frac{\pi}{6}\right) < \sin\theta < \sin\left(\frac{\pi}{2}\right) \implies \frac{\pi}{6} < \theta < \frac{\pi}{2} \).
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