# Example 29 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 29 Differentiate the following w.r.t. x: (i) 𝑒–𝑥 Let 𝑦 = 𝑒–𝑥 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦𝑑𝑥 = 𝑑 𝑒−𝑥𝑑𝑥 𝑑 𝑦𝑑𝑥 = 𝑒−𝑥 . 𝑑 −𝑥𝑑𝑥 𝑑 𝑦𝑑𝑥 = 𝑒−𝑥 (−1) . 𝒅 𝒚𝒅𝒙 = −𝒆−𝒙 Example 29 Differentiate the following w.r.t. x: (ii) sin(log𝑥), 𝑥 > 0 Let 𝑦 =sin(log𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑦𝑑𝑥 = 𝑑 sin( log𝑥) 𝑑𝑥 𝑑𝑦𝑑𝑥 = cos(log𝑥) . 𝑑 log𝑥 𝑑𝑥 𝑑𝑦𝑑𝑥 = cos(log𝑥) . 1𝑥 𝒅𝒚𝒅𝒙 = 𝒄𝒐𝒔(𝒍𝒐𝒈𝒙) 𝒙 Example 29 Differentiate the following w.r.t. x: (iii) 𝑐𝑜𝑠−1(ex) Let 𝑦 = 𝑐𝑜𝑠−1(ex) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑦𝑑𝑥 = 𝑑 cos−1 𝑒𝑥𝑑𝑥 𝑑𝑦𝑑𝑥 = −1 1 − 𝑒𝑥2 . 𝑑 𝑒𝑥𝑑𝑥 𝑑𝑦𝑑𝑥 = −1 1 − 𝑒𝑥2 . 𝑒𝑥 𝒅𝒚𝒅𝒙 = − 𝒆𝒙 𝟏 − 𝒆𝟐𝒙 Example 29 Differentiate the following w.r.t. x: (iv) 𝑒𝑐𝑜𝑠 𝑥 Let 𝑦 = 𝑒 cos𝑥 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑦𝑑𝑥 = 𝑑 𝑒 cos𝑥𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑒 cos𝑥 . 𝑑 cos𝑥𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑒 cos𝑥 . − sin𝑥 𝒅𝒚𝒅𝒙 = − 𝒔𝒊𝒏𝒙. 𝒆 𝒄𝒐𝒔𝒙

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.