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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2010 · Mathematics · Inverse Trigonometric Functions

If y= ^ -1 ((4 x)/(1+4 x^2)) , then what is (d y)/(d x) equal to?

If y=sin⁡−1(4x1+4x2)y=\sin ^{-1}\left(\frac{4 x}{1+4 x^2}\right), then what is dydx\frac{d y}{d x} equal to?

Options

  1. A11+4x2\frac{1}{1+4 x^2}
  2. B−11+4x2-\frac{1}{1+4 x^2}
  3. C41+4x2\frac{4}{1+4 x^2}
  4. D4x1+4x2\frac{4 x}{1+4 x^2}

Correct answer

C. 41+4x2\frac{4}{1+4 x^2}

Step-by-step solution

y=\sin ^{-1}[2(2x)1+(2x)2]\left[\frac{2(2 x)}{1+(2 x)^2}\right] Put 2x=tan⁡θ2 x=\tan \theta ∴y=sin⁡−1[2tan⁡θ1+tan⁡2θ]⇒y=2×tan⁡−1θ∴dydx=2×21+4x2\begin{aligned} & \therefore y=\sin ^{-1}\left[\frac{2 \tan \theta}{1+\tan ^2 \theta}\right] \\ & \Rightarrow y=2 \times \tan ^{-1} \theta \therefore \frac{d y}{d x}=\frac{2 \times 2}{1+4 x^2} \end{aligned}
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