TS EAMCET · Maths · Differentiation
If \(y=\left(\operatorname{Sin}^{-1} x\right)^2\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=\)
- A \(\frac{1}{2}\)
- B \(2\)
- C \(-\frac{1}{2}\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} = 2 (\operatorname{Sin}^{-1} x) \frac{1}{\sqrt{1-x^2}}\) \(\sqrt{1-x^2} \frac{d y}{d x} = 2 \operatorname{Sin}^{-1} x\) \(\frac{-x}{\sqrt{1-x^2}} \frac{d y}{d x} + \sqrt{1-x^2} \frac{d^2 y}{d x^2} = \frac{2}{\sqrt{1-x^2}}\)…
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