A) \[0\]
B) \[1/2\]
C) \[-1/2\]
D) \[3/4\]
Correct Answer: D
Solution :
| Let \[y={{\cos }^{-1}}\left( \sin \sqrt{\frac{1+x}{2}} \right)+{{x}^{x}}\] |
| \[={{\cos }^{-1}}\cos \left( \frac{\pi }{2}-\sqrt{\frac{1+x}{2}} \right)+{{x}^{x}}=\frac{\pi }{2}-\sqrt{\frac{1+x}{2}}+{{x}^{x}}\] |
| \[f'(x)=\frac{dy}{dx}=0-\frac{1}{2\sqrt{\frac{1+x}{2}}}\times \frac{1}{2}+{{x}^{x}}(1+\log x)\] |
| At \[x=1\,f'(x)=-\frac{1}{2\sqrt{\frac{1+1}{2}}}\times \frac{1}{2}+1(1+0)\] |
| \[=-\frac{1}{4}+1=3/4\] |
You need to login to perform this action.
You will be redirected in
3 sec
