Example 26 (iii) - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Examples
Example 1
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Transcript
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)
