MCQ
The first derivative of the function $\left[ {{{\cos }^{ - 1}}\left( {\sin \sqrt {{{1 + x} \over 2}} } \right) + {x^x}} \right]$ with respect to $x$ at $x = 1$ is
- ✓$3/4$
- B$0$
- C$-1/2$
- D$1/2$
$f(x) = \frac{\pi }{2} - \sqrt {\frac{{1 + x}}{2}} + {x^x}$
$\therefore f'(x) = - \frac{1}{{\sqrt 2 }}.\frac{1}{{2\sqrt {1 + x} }} + {x^x}(1 + \log x)$
$f'(1) = - \frac{1}{4} + 1 = \frac{3}{4}$.
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