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