AP EAMCET · Maths · Differentiation
If \(f(x)=\cot ^{-1}\left(\frac{x^x-x^{-x}}{2}\right)\), then \(f^{\prime}(1)=\)
- A -log2
- B log2
- C 1
- D -1
Answer & Solution
Correct Answer
(D) -1
Step-by-step Solution
Detailed explanation
Given, \[ \begin{gathered} f(x)=\cot ^{-1}\left(\frac{x^x-x^{-x}}{2}\right) \\ y=\cot ^{-1}\left(\frac{x^{2 x}-1}{2 \cdot x^x}\right) \end{gathered} \] Put \(x^x=\tan \theta\)…
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