AP EAMCET · Maths · Differentiation
The derivative of \(f(x)=\cos ^{-1}\left[\sin \sqrt{\frac{1+x}{2}}\right]+x^x\) with respect to \(x\) at \(x=1\) is equal to
- A 1
- B \(\frac{1}{4}\)
- C \(\frac{3}{4}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} f(x) & =\cos ^{-1}\left(\sin \sqrt{\frac{1+x}{2}}\right)+x^x \\ & =\frac{\pi}{2}-\sin ^{-1}\left(\sin \sqrt{\frac{1+x}{2}}\right)+x^x \\ & =\frac{\pi}{2}-\sqrt{\frac{1+x}{2}}+x^x \end{aligned}\)…
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