TS EAMCET · Maths · Differentiation
If \(\sec \left(\log _2 y^2\right)=\operatorname{cosec}\left(\log _2 x^2\right)\), then \(\frac{d y}{d x}=\)
- A \(\frac{x}{y}\)
- B \(\frac{y}{x}\)
- C \(-\frac{y}{x}\)
- D \(-\frac{x}{y}\)
Answer & Solution
Correct Answer
(C) \(-\frac{y}{x}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \sec \left(\log _2 y^2\right)=\operatorname{cosec}\left(\log _2 x^2\right) \\ & \Rightarrow \sec \left(2 \log _2 y\right)=\operatorname{cosec}\left(2 \log _2 x\right) \\ & \Rightarrow \sec ^2\left(2 \log _2 y\right)=\operatorname{cosec}^2\left(2 \log _2…
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