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Example 26 Differentiate the following w.r.t. x: (iii) 〖𝑐𝑜𝑠〗^(−1) "(ex)" Let 𝑦 = 〖𝑐𝑜𝑠〗^(−1) "(ex)" Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(cos^(−1)⁡(𝑒^𝑥 ) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = (−1)/√(1 − (𝑒^𝑥 )^2 ) . 𝑑(𝑒^𝑥 )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = (−1)/√(1 − (𝑒^𝑥 )^2 ) . 𝑒^𝑥 𝒅𝒚/𝒅𝒙 = (−𝒆^𝒙)/√(𝟏 − 𝒆^𝟐𝒙 ) (As (cos^(−1)⁡𝑥 )^′=(−1)/√(1 − 𝑥^2 )) (As(𝑒^𝑥 )^′=𝑒^𝑥)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.