Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Deleted for CBSE Board 2024 Exams

Question 4 Important Deleted for CBSE Board 2024 Exams

Question 5 Deleted for CBSE Board 2024 Exams

Question 6 Important Deleted for CBSE Board 2024 Exams

Last updated at June 2, 2023 by Teachoo

Example 43 Differentiate 〖𝑠𝑖𝑛〗^2 𝑥 𝑤.𝑟.𝑡. 𝑒^(cos𝑥 ". " )Let 𝑢 = 〖𝑠𝑖𝑛〗^2 𝑥 & 𝑣 =𝑒^(cos𝑥 ) We need to differentiate 𝑢 𝑤.𝑟.𝑡. 𝑣 . i.e., 𝑑𝑢/𝑑𝑣 Here, 𝒅𝒖/𝒅𝒗 = (𝒅𝒖/𝒅𝒙)/(𝒅𝒗/𝒅𝒙) Calculating 𝒅𝒖/𝒅𝒙 𝑢 = 〖𝑠𝑖𝑛〗^2 𝑥 Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑢/𝑑𝑥 = 𝑑(〖𝑠𝑖𝑛〗^2 𝑥)/𝑑𝑥 𝑑𝑢/𝑑𝑥 = 2 sin𝑥 . 𝑑(sin𝑥 )/𝑑𝑥 𝑑𝑢/𝑑𝑥 = 𝟐 𝒔𝒊𝒏𝒙 . 𝐜𝐨𝐬𝒙 Calculating 𝒅𝒗/𝒅𝒙 𝑣 =𝑒^(cos𝑥 ) Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑣/𝑑𝑥 = 𝑑(𝑒^(cos𝑥 ) )/𝑑𝑥 𝑑𝑣/𝑑𝑥 = 𝑒^(cos𝑥 ) . 𝑑(cos𝑥 )/𝑑𝑥 𝑑𝑣/𝑑𝑥 = 𝑒^(cos𝑥 ) . (−sin𝑥 ) 𝑑𝑣/𝑑𝑥 = −𝒔𝒊𝒏𝒙. 𝒆^(𝒄𝒐𝒔𝒙 )Therefore 𝑑𝑢/𝑑𝑣 = (𝑑𝑢/𝑑𝑥)/(𝑑𝑣/𝑑𝑥) = (2 sin𝑥" ." cos𝑥)/(−sin𝑥 . 𝑒^(cos𝑥 ) ) = (−𝟐"." 𝒄𝒐𝒔𝒙)/𝒆^(𝒄𝒐𝒔𝒙 )