QJEEM19Maf914: JEE Main 2019 Mathematics - Class 12 JEEM19Maf914 Solution: If  xlog e (log e x) − x 2 + y 2 = 4(y > 0), then d y d x…

Question

Verified Solution • 2025–26 Session moderate

If xlog_e(log_ex)

-

x² + y² = 4(y > 0), then

\frac{d y}{d x}

at x = e is equal to :

Accepted Answer

Differentiating with respect to x,

x . \frac{1}{ℓ n x} . \frac{1}{x} + ℓ n (ℓ n x) - 2 x + 2 y . \frac{d y}{d x} = 0

at

x = e

we get

1 - 2 e + 2 y \frac{d y}{d x} = 0 \Rightarrow \frac{d y}{d x} = \frac{2 e - 1}{2 y}

\Rightarrow \frac{d y}{d x} = \frac{2 e - 1}{2 \sqrt{4 + e^{2}}}

as

y (e) = \sqrt{4 + e^{2}}

QJEEM19Maf914: JEE Main 2019 Mathematics - Class 12 JEEM19Maf914 Solution: If &nbsp;xlog e (log e x) − x 2 + y 2 = 4(y > 0), then d y d x…