JEE Main 2017MathematicsDifferentiationMediumMCQ

JEE Main 2017 — Differentiation Question with Solution

JEE Main 2017 (02 Apr)

Question

If for x∈0,14, the derivative of tan-1⁡6xx1-9x3 is x ⋅gx , then gx equals:

Choose an option

Show full solutionCorrect option: A
Correct answer
A91+9x3

Step-by-step explanation

Let  3x32=y, then y∈0,38

 tan-1⁡6xx1-9x3=tan-1⁡2y1-y2

⇒ 2tan-1⁡y=2tan-1⁡3x32

Now ⇒ddx2tan-1⁡3x32=21+9x3⋅3⋅32⋅x12

⇒ddx2tan-1⁡3x32=91+9x3 ⋅ x

⇒x.gx=91+9x3 ⋅ x

⇒gx=91+9x3

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About this question

This is a previous-year question from JEE Main 2017, covering the Differentiation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.