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AP EAMCET · Maths · Differentiation

If \(y=\sin ^{-1}\left[x \sqrt{1-x}-\sqrt{x} \cdot \sqrt{1-x^2}\right]\) and \(0 < x < 1\), then \(\frac{d y}{d x}\) is equal to

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

Answer & Solution

Correct Answer

(B) \(\frac{1}{\sqrt{1-x^2}}-\frac{1}{2 \sqrt{x-x^2}}\)

Step-by-step Solution

Detailed explanation

We have,…