Misc 8 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 16, 2024 by Teachoo

Misc 8 - Differentiate cos (a cos x + b sin x) - Chapter 5 Class 12 - Miscellaneous

part 2 - Misc 8 - Miscellaneous - Serial order wise - Chapter 5 Class 12 Continuity and Differentiability

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Transcript

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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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