AP EAMCET · Maths · Differentiation
If \(x=e^{y+e^{y+e^{y+\ldots}}}\), then \(\frac{d y}{d x}=\)
- A \(\frac{1-x}{x}\)
- B \(\frac{1}{x}\)
- C \(\frac{x}{1+x}\)
- D \(\frac{1+x}{x}\)
Answer & Solution
Correct Answer
(A) \(\frac{1-x}{x}\)
Step-by-step Solution
Detailed explanation
It is given that, \(\begin{array}{lll} & x =e^{y+e^{y+e^{y+\ldots}}} \\ \Rightarrow & x =e^{y+x} \\ \Rightarrow & \log _e x =x+y \Rightarrow y=\log _e x-x \end{array}\) On differentiating both sides with respect to ' \(x\) ', we get…
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