JEE Main 2019 — Differentiation Question with Solution
From: JEE Main 2019 (Online) 8th April Evening Slot
Question
If ƒ(1) = 1, ƒ'(1) = 3, then the derivative of
ƒ(ƒ(ƒ(x))) + (ƒ(x))2
at x = 1 is :
Choose an option
Show full solutionCorrect option: A
Correct answer
A33
Step-by-step explanation
Given ƒ(1) = 1, ƒ'(1) = 3
Let y = ƒ(ƒ(ƒ(x))) + (ƒ(x))2
On differentiating both sides with respect to x we get,
= ƒ'(ƒ(ƒ(x))).ƒ'(ƒ(x)).ƒ'(x) + 2ƒ(x).ƒ'(x)
Now at x = 1,
= ƒ'(ƒ(ƒ(1))).ƒ'(ƒ(1)).ƒ'(1) + 2ƒ(1).ƒ'(1)
= ƒ'(ƒ(1)).ƒ'(1).ƒ'(1) + 2.1.ƒ'(1)
= ƒ'(1).ƒ'(1).ƒ'(1) + 2.1.ƒ'(1)
= 333 + 23
= 33
Let y = ƒ(ƒ(ƒ(x))) + (ƒ(x))2
On differentiating both sides with respect to x we get,
= ƒ'(ƒ(ƒ(x))).ƒ'(ƒ(x)).ƒ'(x) + 2ƒ(x).ƒ'(x)
Now at x = 1,
= ƒ'(ƒ(ƒ(1))).ƒ'(ƒ(1)).ƒ'(1) + 2ƒ(1).ƒ'(1)
= ƒ'(ƒ(1)).ƒ'(1).ƒ'(1) + 2.1.ƒ'(1)
= ƒ'(1).ƒ'(1).ƒ'(1) + 2.1.ƒ'(1)
= 333 + 23
= 33
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This is a previous-year question from JEE Main 2019, 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.