Question 23
The derivative of cos–1 (2x2 – 1) w.r.t. cos–1x is
(A) 2 (B) (−1)/(2√(1−𝑥^2 ))
(C) 2/𝑥 (D) 1 − x2
Let 𝑦=〖𝑐𝑜𝑠〗^(−1)𝑥
cos〖𝑦=𝑥〗
〖𝒙=𝒄𝒐𝒔〗𝒚
We need to find derivative of
〖𝑐𝑜𝑠〗^(−1)〖(2𝑥−1)〗 w.r.t. 〖𝑐𝑜𝑠〗^(−1)𝑥
i.e., 〖𝒄𝒐𝒔〗^(−𝟏)〖(𝟐𝒙−𝟏)〗 w.r.t. 𝒚
i.e., (𝒅 〖(〖𝒄𝒐𝒔〗^(−𝟏)〗〖(𝟐𝒙−𝟏)〗))/𝒅𝒚
Finding (𝒅 〖(〖𝒄𝒐𝒔〗^(−𝟏)〗〖(𝟐𝒙^𝟐 − 𝟏)〗))/𝒅𝒚
(𝒅 〖(〖𝒄𝒐𝒔〗^(−𝟏)〗〖(𝟐𝒙^𝟐 − 𝟏)〗))/𝒅𝒚
Putting 〖𝒙=𝒄𝒐𝒔〗𝒚
= (𝑑 〖(〖𝑐𝑜𝑠〗^(−1)〗〖(2 〖𝒄𝒐𝒔〗^𝟐𝒚 − 1)〗))/𝑑𝑦
Using 𝒄𝒐𝒔〖𝟐𝜽=𝟐〖𝒄𝒐𝒔〗^𝟐 𝜽−𝟏〗
=(𝑑 〖(〖𝑐𝑜𝑠〗^(−1)〗〖(𝐜𝐨𝐬𝟐𝒚)〗))/𝑑𝑦
=(𝑑(2𝑦))/𝑑𝑦
=𝟐
So, the correct answer is (A)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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