NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If x y . y x = 16 , then the value of d y d x at ( 2 , 2 ) is

Options

A- 1
B0
C1
DNone of these

Correct answer

A. - 1

Step-by-step solution

Since, x y . y x = 16 ∴ log e ⁡ x y + log e ⁡ y x = log e ⁡ 16 ⇒ y log e ⁡ x + x log e ⁡ y = 4 log e ⁡ 2 Now, on differentiating both sides w.r.t. x , we get y x + log e ⁡ x d y d x + x y d y d x + log e ⁡ y . 1 = 0 ⇒ d y d x = - log e ⁡ y + y x log e ⁡ x + x y ∴ d y d x ( 2,2 ) = - ( log e ⁡ 2 + 1 ) ( log e ⁡ 2 + 1 ) = - 1

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