Question

The first derivative of the function \( \left( \cos^{-1}\left(\sin\sqrt{\frac{1+x}{2}}\right) + x^x \right) \) with respect to \( x \) at \( x = 1 \) is

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

Hint:

Remember: \(\frac{d}{dx}(x^x) = x^x(1 + \log x)\).

Answer 1

The Correct Option is D