If x = e y + e y + ..10∞ , x > 0 , then d x d y is

x = e y + e y + e y + …… ∞ ⇒ x = e y + x ⇒ ln x − x = y ⇒ d x d y = x 1 − 1 = x 1 − x

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MathematicsDifferentiationDifferentiation of composite functionsMedium2 minPYQ_2004

MathematicsMediumsingle choice

If $x = e^{y + e^{y + ..10\infty}}, x > 0$ , then $\frac{d y}{d x}$ is

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Answer:

Solution:

$x = e^{y + e^{y + e^{y + \dots\dots \infty}}} \Rightarrow x = e^{y + x}$ $\Rightarrow ln x - x = y \Rightarrow \frac{d y}{d x} = \frac{1}{x} - 1 = \frac{1 - x}{x}$

Stream:JEESubject:MathematicsTopic:DifferentiationSubtopic:Differentiation of composite functions

⏱ 2mℹ️ Source: PYQ_2004

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