JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(\log _e y=3 \sin ^{-1} x\), then \((1-x)^2 y^{\prime \prime}-x y^{\prime}\) at \(x=\frac{1}{2}\) is equal to :
- A \(9 e^{\pi / 6}\)
- B \(3 e^{\pi / 6}\)
- C \(3 e^{\pi / 2}\)
- D \(9 e^{\pi / 2}\)
Answer & Solution
Correct Answer
(D) \(9 e^{\pi / 2}\)
Step-by-step Solution
Detailed explanation
\( \ln (y)=3 \sin ^{-1} x \) \( \frac{1}{y} \cdot y^{\prime}=3\left(\frac{1}{\sqrt{1-x^2}}\right) \) \( \Rightarrow y^{\prime}=\frac{3 y}{\sqrt{1-x^2}} \text { at } x=\frac{1}{2} \)…
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