TS EAMCET · Maths · Differentiation
If \(f(x)=\frac{(x+1) \sinh x}{e^{2 x} \tan x}\) and \(\frac{f^{\prime}(x)}{f(x)}=\frac{1}{x+1}+\operatorname{coth} x+g(x)\), then \(g(x)=\)
- A \(-2+\frac{1}{\sin x \cos x}\)
- B \(2-2 \operatorname{cosec} 2 x\)
- C \(-2(1+\operatorname{cosec} 2 x)\)
- D \(2-\frac{1}{\sin x \cos x}\)
Answer & Solution
Correct Answer
(C) \(-2(1+\operatorname{cosec} 2 x)\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)=\frac{(x+1) \sinh x}{e^{2 x} \tan x}=(x+1) \sinh x e^{-2 x} \cot x\)…
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