If , then find .
If $x = e^{y + e^{y + e^{y + \dots \infty}}}$, $x > 0$ then find $\frac{dy}{dx}$.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Given $x = e^{y + e^{y + e^{y + \dots \infty}}}$, we can write $x = e^{y + x}$.
Taking natural logarithm on both sides:
$\ln x = y + x$
Differentiating both sides with respect to $x$:
$\frac{1}{x} = \frac{dy}{dx} + 1$
$\frac{dy}{dx} = \frac{1}{x} - 1 = \frac{1 - x}{x}$
From ISC 2026 Mathematics Paper 1, question 1(xii).