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TS EAMCET · Maths · Differentiation

If \(y=\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\log \sqrt{1-x^2}\), then \(\frac{d y}{d x}=\)

  1. A \(\frac{\sin ^{-1} x}{1-x^2}\)
  2. B \(\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}\)
  3. C \(\frac{x}{1-x^2}\)
  4. D \(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}-\frac{2 x}{\sqrt{1-x^2}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}\)

Step-by-step Solution

Detailed explanation

We have, \(y=\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\log \sqrt{1-x^2}\) \(\left[1 \cdot \sin ^{-1} x+\frac{x}{\sqrt{1-x^2}}\right] \sqrt{1-x^2}-x \sin ^{-1} x\)…