CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

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 Sept. 4, 2021 by Teachoo

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

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)

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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.