Question

If `x = e^(y + e^(y + e^(y + ...∞)))` x > 0 then find `dy/dx`.

Answer 1

x = e^{y + x   ...[Simplify]}

log x = y + x   ...[Taking natural log on both sides]

d.w.r. to x

`1/x = dy/dx`

`dy/dx = 1/x −1`   ...[Differentiating both sides with respect to x]

= `(1 − x)/x`

`dy/dx = (1 − x)/x`