AP EAMCET · Maths · Differentiation
\(\frac{d}{d x}\left(\log \left(\sqrt{x+\sqrt{x^2+a^2}}\right)\right)=\)
- A \(\sqrt{x^2+a^2}\)
- B \(\frac{1}{\sqrt{x^2+a^2}}\)
- C \(\frac{1}{2 \sqrt{x^2+a^2}}\)
- D \(\frac{1}{2\left(x+\sqrt{x^2+a^2}\right)}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2 \sqrt{x^2+a^2}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \frac{d}{d x}\left(\log \left(\sqrt{x+\sqrt{x^2+a^2}}\right)\right) \\ &= \frac{1}{\sqrt{x+\sqrt{x^2+a^2}}} \times\left(\frac{1}{2 \sqrt{x+\sqrt{x^2+a^2}}}\right) \\ & \times\left(1+\frac{1}{2} \cdot \frac{2 x}{\sqrt{x^2+a^2}}\right) \\…
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