JEE Main 2018 — Differentiation Question with Solution
From: JEE Main 2018 (Online) 15th April Morning Slot
Question
If f\left( x \right) = \left| {\matrix{
{\cos x} & x & 1 \cr
{2\sin x} & {{x^2}} & {2x} \cr
{\tan x} & x & 1 \cr
} } \right|, then
Choose an option
Show full solutionCorrect option: D
Correct answer
Dexists and is equal to 2.
Step-by-step explanation
Given,
f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|
= cosx(x2 - 2x2) - x(2 sinx - 2x tanx) + (2x sinx - x2 tanx)
= x2 (tanx - cosx)
= 2x (tanx - cosx) + x2(sec2x + sinx)
=
=
= 2 (0-1) + 0
= -2
f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|
= cosx(x2 - 2x2) - x(2 sinx - 2x tanx) + (2x sinx - x2 tanx)
= x2 (tanx - cosx)
= 2x (tanx - cosx) + x2(sec2x + sinx)
=
=
= 2 (0-1) + 0
= -2
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This is a previous-year question from JEE Main 2018, 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.