TS EAMCET · Maths · Differentiation
If \(y=\cos ^{-1}\left(\frac{a^2-x^2}{a^2+x^2}\right)+\sin ^{-1}\left(\frac{2 a x}{a^2+x^2}\right)\), then \(\frac{d y}{d x}\) is equal to
- A \(\frac{a}{x^2+a^2}\)
- B \(\frac{2 a}{x^2+a^2}\)
- C \(\frac{4 a}{x^2+a^2}\)
- D \(\frac{a^2}{x^2+a^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{4 a}{x^2+a^2}\)
Step-by-step Solution
Detailed explanation
\(y=\cos ^{-1}\left(\frac{a^2-x^2}{a^2+x^2}\right)+\sin ^{-1}\left(\frac{2 a x}{a^2+x^2}\right)\) Put \(\quad x=a \tan \theta\) \(\Rightarrow \quad \theta=\tan ^{-1}\left(\frac{x}{a}\right)\) \(y=\cos ^{-1}\left(\frac{a^2-a^2 \tan ^2 \theta}{a^2+a^2 \tan ^2 \theta}\right)\)…
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