Let's Differentiate

Calculus Level 4

\[\large y = \left[(\log_{\cos x} \sin x) \cdot (log_{\sin x} \cos x)^{-1} + sin^{-1} \left( \dfrac{2x}{1 + x^2}\right)\right] \]

Find the derivative with respect to x of the above function at \( x = \dfrac{\pi}{4}\)

Details:

  • You may use calculator for the final calculations.
  • Use \(ln 2 \simeq 0.7 \) and \( \pi \simeq 3.1 \)
  • Put the answer upto 2 decimal places.
(Source = IITJEE 19**)
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