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COMEDK · Maths · 26. Differentiation

\(\text { If } y=\tan ^{-1}\left(\dfrac{3-2 x}{1+6 x}\right) \text { then } \dfrac{d y}{d x} \text { is }\)

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

Answer & Solution

Correct Answer

(A) \(-\dfrac{2}{1+4 x^2}\)

Step-by-step Solution

Detailed explanation

The given expression is \(y = \tan^{-1}\left(\dfrac{3-2x}{1+6x}\right)\). We can rewrite the argument of the inverse tangent function as follows: \(\dfrac{3-2x}{1+6x} = \dfrac{3-2x}{1+(3)(2x)}\) Using the identity…