Question 24 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at May 29, 2023 by Teachoo

The derivative of sin−1 (2x √(1 - x
^{
2
}
)) w.r.t sin−1 x, 1/√2 < π₯ < 1, is:

(a) 2 (b) π/2 − 2
(c) π/2 (d) −2

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Question 24 The derivative of sinβ1 ("2π₯" β("1 β " π₯^2 )) w.r.t sinβ1 x, 1/β2 < π₯ < 1, is: (a) 2 (b) π/2 β 2 (c) π/2 (d) β2
Let y = sinβ1 x
sin y = x
x = sin y
We need to find the derivative of
sinβ1 ("2π₯" β("1 β " π₯^2 )) w.r.t sinβ1 x
i.e. sinβ1 ("2π₯" β("1 β " π₯^2 )) w.r.t y
i.e. (π (γπ¬π’π§γ^(βπ)β‘γ(ππβ(π β π^π ))) γ)/π π
Now,
(π(sin^(β1)β‘γ(2π₯β(1 β π₯^2 ))) γ)/ππ¦
Putting x = sin y
= (π(sin^(β1)β‘γ(2 sinβ‘π¦ β(1 β γπ ππγ^2 π¦))) γ)/ππ¦
= (π(sin^(β1)β‘γ(2 sinβ‘π¦ β(cos^2β‘π¦ )))γ)/ππ¦
= (π(sin^(β1)β‘γ(2 sinβ‘π¦ cosβ‘π¦ ))γ)/ππ¦
= (π(sin^(β1)β‘γ(sinβ‘2π¦ ))γ)/ππ¦
= π(2π¦)/ππ¦
= 2
So, the correct answer is (A)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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