Misc 8 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Last updated at Aug. 13, 2021 by Teachoo

Misc 8 - Miscellaneous

Misc 8 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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