TS EAMCET · Maths · Differentiation
If \(y=\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\ldots \infty}}}\), then \(\frac{d y}{d x}=\)
- A \(\frac{\cos (\log 2 x)}{2 x(2 y-1)}\)
- B \(\frac{\cos (\log 2 x)}{(2 y-1)}\)
- C \(\frac{\cos (\log 2 x)}{x(2 y-1)}\)
- D \(\frac{\sin (\log 2 x)}{x(2 y-1)}\)
Answer & Solution
Correct Answer
(C) \(\frac{\cos (\log 2 x)}{x(2 y-1)}\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}y=\sqrt{\sin (\log (2 x))+y} \Rightarrow y^2-y=\sin (\log 2 x) \\ \Rightarrow(2 y-1) y^{\prime}=\frac{\cos (\log 2 x)}{2 x} \times 2 \Rightarrow \frac{d y}{d x}=\frac{\cos (\log 2 x)}{x(2 y-1)} .\end{gathered}\)
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