Misc 8 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 13, 2021 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.