AP EAMCET · Maths · Differentiation
If \(y=\sqrt{2 x+\cos ^2\left(2 x+\frac{\pi}{4}\right)}\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{4}\).
- A \(\frac{2 \sqrt{2}}{\sqrt{\pi+1}}\)
- B \(2 \sqrt{\pi+1}\)
- C \(\frac{2}{\sqrt{\pi+1}}\)
- D \(\frac{\sqrt{2}}{\sqrt{\pi+1}}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 \sqrt{2}}{\sqrt{\pi+1}}\)
Step-by-step Solution
Detailed explanation
Given, \(y=\sqrt{2 x+\cos ^2\left(2 x+\frac{\pi}{4}\right)}\) So, at \(x=\frac{\pi}{4}\) \(\begin{aligned} y & =\sqrt{\frac{\pi}{2}+\cos ^2\left(\frac{\pi}{2}+\frac{\pi}{4}\right)} \\ & =\sqrt{\frac{\pi}{2}+\sin ^2 \frac{\pi}{4}}=\sqrt{\frac{\pi}{2}+\frac{1}{2}} \end{aligned}\)…
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