NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If l n x + y = 2 x y , then y ′ 0 is equal to

Options

A1
B− 1
C2
D0

Correct answer

A. 1

Step-by-step solution

Given equation is ln ( x + y ) = 2 x y ...(1) For x = 0 ln ( 0 + y ) = 2.0. y = 0 ⇒ ln y = 0 ⇒ y = 1 Now, differentiating (1), we get, 1 x + y 1 + d y d x = 2 y + 2 x d y d x At point (0,1), we get, 1 0 + 1 1 + d y d x = 2 1 + 2 . 0 . d y d x ⇒ 1 + d y d x = 2 ⇒ d y d x = 1 = y ' ( 0 )

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