Ex 5.2, 7 - Differentiate 2 root cot (x^2) - Teachoo - Ex 5.2

Ex 5.2, 7 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Ex 5.2, 7 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

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Transcript

Ex 5.2, 7 Differentiate the functions with respect to 𝑥 2√(cot ( 𝑥2 ))Let 𝑦 = " " 2√(cot ( 𝑥2 )) We need to find derivative of 𝑦 𝑤.𝑟.𝑡.𝑥 𝑦′ = (2√(cot ( 𝑥^2 ) ) )^′ = 2 × 1/(2√(cot ( 𝑥^2 ) )) . (cot ( 𝑥^2 ))^′ = 1/√(cot ( 𝑥^2 ) ) . (−𝑐𝑜𝑠𝑒𝑐^2 (𝑥^2 )) . ( 𝑥^2 )^′ = 1/√(cot ( 𝑥^2 ) ) . (−𝑐𝑜𝑠𝑒𝑐^2 (𝑥^2)) . 2𝑥 = (−2𝑥" " 𝑐𝑜𝑠𝑒𝑐^2 𝑥^2)/√(cot ( 𝑥^2 ) ) = (−2𝑥)/(sin^2⁡(𝑥^2 ) . √( 〖cos 〗⁡〖(𝑥^2)〗/〖sin 〗⁡〖(𝑥^2)〗 ) ) "= " (−2𝑥)/(〖𝑠𝑖𝑛 〗⁡(𝑥^2 ) × 〖𝒔𝒊𝒏 〗⁡(𝒙^𝟐 ) √( 〖cos 〗⁡〖(𝑥^2)〗/〖sin 〗⁡〖(𝑥^2)〗 ) ) " " = (− 2𝑥 )/(〖sin 〗⁡〖(𝑥)^2 〗 ×√(〖〖𝒔𝒊𝒏〗^𝟐 〗⁡〖(𝒙^𝟐)〗 × 〖cos 〗⁡〖(𝑥^2)〗/sin⁡〖 (𝑥^2)〗 )) = (− 2𝑥 )/(〖sin 〗⁡〖(𝑥)^2 〗 ×√(〖𝐜𝐨𝐬 〗⁡〖(𝒙^𝟐)〗 𝒔𝒊𝒏⁡〖 (𝒙^𝟐)〗 )) = (− 2𝑥 )/(〖sin 〗⁡〖(𝑥)^2 〗 ×√(2/2 × 〖cos 〗⁡〖(𝑥^2)〗 sin⁡〖 (𝑥^2)〗 )) = (− 2√𝟐 𝑥 )/(〖sin 〗⁡〖(𝑥)^2 〗 ×√(2 〖cos 〗⁡〖(𝑥^2)〗 sin⁡〖 (𝑥^2)〗 )) = (− 𝟐√𝟐 𝒙 )/(〖𝐬𝐢𝐧 〗⁡〖(𝒙)^𝟐 〗 ×√(〖𝒔𝒊𝒏 〗⁡〖(𝟐𝒙^𝟐)〗 )) (As sin 2θ = 2 sin θ cos θ)

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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.