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AP EAMCET · Maths · Differentiation

If \(2 f(x)-3 f\left(\frac{1}{x}\right)=x+1\), then \(f^{\prime}(\sqrt{3})\) is equal to

  1. A \(\frac{-1}{5}\)
  2. B \(\frac{3}{5}\)
  3. C \(\frac{-\sqrt{3}}{5}\)
  4. D \(\frac{\sqrt{3}}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{-1}{5}\)

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & \text { } 2 f(x)-3 f\left(\frac{1}{x}\right)=x+1...(i) \\ & \text { Replace } x \rightarrow \frac{1}{x} \\ & 2 f\left(\frac{1}{x}\right)-3 f(x)=\frac{1}{x}+1...(ii) \end{aligned} \] Multiply Eq. (i) by 2 and Eq. (ii) by 3 and then adding…