The derivative of cos ^{ –1 } (2x ^{ 2 } – 1) w.r.t. cos ^{ –1 } x is
(A) 2
(B) (-1)/(2√(1-x ^{ 2 } ))
(C) 2/x
(D) 1 − x ^{ 2 }
This question is similar to Question 24 - CBSE Class 12 - Sample Paper for 2022 Boards
Last updated at Nov. 18, 2021 by Teachoo
This question is similar to Question 24 - CBSE Class 12 - Sample Paper for 2022 Boards
Transcript
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)
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