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Derivative of sec-1 x (Sec inverse x) - Teachoo [with Video]

Derivative of sec-1 x (Sec inverse x) - Part 2


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Derivative of 〖𝒔𝒆𝒄〗^(βˆ’πŸ) 𝒙 𝑓 (π‘₯)=〖𝑠𝑒𝑐〗^(βˆ’1) π‘₯ Let π’š= 〖𝒔𝒆𝒄〗^(βˆ’πŸ) 𝒙 sec⁑〖𝑦=π‘₯γ€— 𝒙=π¬πžπœβ‘γ€–π’š γ€— Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑π‘₯/𝑑π‘₯ = (𝑑 (sec⁑𝑦 ))/𝑑π‘₯ 1 = (𝑑 (sec⁑𝑦 ))/𝑑π‘₯ Γ— 𝑑𝑦/𝑑𝑦 1 = (𝑑 (sec⁑𝑦 ))/𝑑𝑦 Γ— 𝑑𝑦/𝑑π‘₯ 1 = π’•π’‚π’β‘π’š .π’”π’†π’„β‘π’š. 𝑑𝑦/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = 1/(π’•π’‚π’β‘π’š .γ€– sec〗⁑𝑦 ) 𝑑𝑦/𝑑π‘₯ = 1/((√(γ€–π¬πžπœγ€—^πŸβ‘π’š βˆ’ 𝟏)) .γ€– sec〗⁑𝑦 ) Putting value of 𝑠𝑒𝑐⁑𝑦 = π‘₯ 𝑑𝑦/𝑑π‘₯ = 1/((√(π‘₯^2 βˆ’ 1 ) ) . π‘₯) 𝑑𝑦/𝑑π‘₯ = 1/(π‘₯ √(π‘₯^2 βˆ’ 1 ) ) Hence 𝒅(〖𝒔𝒆𝒄〗^(β€“πŸ) 𝒙)/𝒅𝒙 = 𝟏/(𝒙 √(𝒙^𝟐 βˆ’ 𝟏 ) ) As tan2 ΞΈ = sec2 ΞΈ – 1, tan ΞΈ = √("sec2 ΞΈ – 1" ) As 𝑦 = 〖𝑠𝑒𝑐〗^(βˆ’1) π‘₯ So, π’”π’†π’„β‘π’š = 𝒙

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.