TS EAMCET · Maths · Differentiation
If \(y=\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\log \sqrt{1-x^2}\), then \(\frac{d y}{d x}=\)
- A \(\frac{\sin ^{-1} x}{1-x^2}\)
- B \(\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}\)
- C \(\frac{x}{1-x^2}\)
- D \(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}-\frac{2 x}{\sqrt{1-x^2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}\)
Step-by-step Solution
Detailed explanation
We have, \(y=\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\log \sqrt{1-x^2}\) \(\left[1 \cdot \sin ^{-1} x+\frac{x}{\sqrt{1-x^2}}\right] \sqrt{1-x^2}-x \sin ^{-1} x\)…
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