Misc 8 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at June 5, 2023 by Teachoo

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Misc 8 Differentiate 𝑤.𝑟.𝑡. 𝑥 the function, cos ⁡(𝑎 cos⁡𝑥+𝑏 sin⁡𝑥), for some constant 𝑎 and 𝑏. Let 𝑦 = cos ⁡(𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦/𝑑𝑥 = (𝑑(cos((a cos⁡x+b sin⁡x )))/𝑑𝑥 𝑑𝑦/𝑑𝑥 = −sin⁡𝑥 (𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) . (𝑑⁡(𝑎 cos⁡𝑥+𝑏 sin⁡𝑥))/𝑑𝑥 = −sin⁡𝑥 (𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) . (𝑎 .𝑑⁡(cos⁡𝑥 )/𝑑𝑥+𝑏 .𝑑⁡(sin⁡𝑥 )/𝑑𝑥) = −sin⁡𝑥 (𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) . (𝑎(−sin⁡𝑥 )+𝑏 (cos⁡𝑥 )) = −sin⁡𝑥 (𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) . (−𝑎 sin⁡𝑥+𝑏 cos⁡𝑥 ) = −sin⁡𝑥 (𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) . −(𝑎 sin⁡𝑥−𝑏 cos⁡𝑥 ) = 𝐬𝐢𝐧⁡〖 (𝒂 𝒄𝒐𝒔⁡𝒙+𝒃 𝒔𝒊𝒏⁡𝒙)" " (𝒂 𝒔𝒊𝒏⁡𝒙−𝒃 𝒄𝒐𝒔⁡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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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