Discussion
If \(\frac{dy}{dx} =\) \(\frac{1}{8(\sqrt{16+\sqrt{25+\sqrt{x}}})(\sqrt{25+\sqrt{x}})\sqrt{x}}\), then \(y =\)
Answer: A
The answer is \(y = \sqrt{16 + \sqrt{25 + \sqrt{x}}} + C\).
Differentiate the candidate with the chain rule, from the outside in.
\[ \begin{aligned} \frac{d}{dx}\sqrt{16 + \sqrt{25 + \sqrt{x}}} &= \frac{1}{2\sqrt{16 + \sqrt{25 + \sqrt{x}}}}\cdot\frac{d}{dx}\sqrt{25 + \sqrt{x}} \\ \frac{d}{dx}\sqrt{25 + \sqrt{x}} &= \frac{1}{2\sqrt{25 + \sqrt{x}}}\cdot\frac{1}{2\sqrt{x}} \end{aligned} \]
The three factors of \(\frac{1}{2}\) give the 8 in the denominator, and the three roots match exactly, so this is the given \(\frac{dy}{dx}\). Adding x or \(x^{2}\), or multiplying by them, would add terms that are not there.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development