99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

Let y = x x x … ∞ , then d y d x is equal to (given x > 0 )

Options

Ay x y - 1
By 2 x ( 1 - y ln x )
Cy x ( 1 + y ln x )
DNone of these

Correct answer

B. y 2 x ( 1 - y ln x )

Step-by-step solution

Given, y = x x x ... ∞ then y = x y Taking ln on both the sides, we get ln y = y ln x ⇒ 1 y . d y d x = y . 1 x + d y d x . ln x ⇒ d y d x 1 y - ln ⁡ x = y x ⇒ d y d x = y 2 x ( 1 - y ln x )

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