If xloge(logex) - x² + y² = 4 (y > 0), then dy/dx at x = e is equal to:

When x = e, then 0 - e² + y² = 4, y = √e²+4
Differentiating with respect to x, We get:
x.1/x + ln(lnx) + 2y.dy/dx = 0
at x = e we get 1 + 2ydy/dx = 0 ⇒ dy/dx = -1/2y ⇒ dy/dx = -1/2√4+e²
As y(e) = √4+e²