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Ex 5.4, 6 - Differentiate ex + ex2 + ex3 + ex4 + ex5 - Finding derivative of Exponential & logarithm functions

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.4, 6 Differentiate 𝑤.𝑟.𝑡. 𝑥 in , 𝑒﷮𝑥﷯+ 𝑒﷮ 𝑥﷮2﷯﷯ + 𝑒﷮ 𝑥﷮3﷯﷯+ 𝑒﷮ 𝑥﷮4﷯﷯ + 𝑒﷮ 𝑥﷮5﷯﷯ Let 𝑦 = 𝑒﷮𝑥﷯+ 𝑒﷮ 𝑥﷮2﷯﷯ +... + 𝑒﷮ 𝑥﷮5﷯﷯ y = 𝑒﷮𝑥﷯+ 𝑒﷮ 𝑥﷮2﷯﷯ + 𝑒﷮ 𝑥﷮3﷯﷯+ 𝑒﷮ 𝑥﷮4﷯﷯ + 𝑒﷮ 𝑥﷮5﷯﷯ Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦﷯﷮𝑑𝑥﷯ = 𝑑 𝑒﷮𝑥﷯+ 𝑒﷮ 𝑥﷮2﷯﷯ + 𝑒﷮ 𝑥﷮3﷯﷯+ 𝑒﷮ 𝑥﷮4﷯﷯ + 𝑒﷮ 𝑥﷮5﷯﷯﷯﷮𝑑𝑥﷯ = 𝑑 𝑒﷮𝑥﷯﷯ ﷮𝑑𝑥﷯ + 𝑑 𝑒﷮ 𝑥﷮2﷯﷯﷯﷮𝑑𝑥﷯ + 𝑑 𝑒﷮ 𝑥﷮3﷯﷯﷯﷮𝑑𝑥﷯ + 𝑑 𝑒﷮ 𝑥﷮4﷯﷯﷯﷮𝑑𝑥﷯ + 𝑑 𝑒﷮ 𝑥﷮5﷯﷯﷯﷮𝑑𝑥﷯ = 𝑒﷮𝑥﷯ + 𝑒﷮ 𝑥﷮2﷯﷯. 𝑑 𝑥﷮2﷯﷯﷮𝑑𝑥﷯ + 𝑒﷮ 𝑥﷮3﷯﷯. 𝑑 𝑥﷮3﷯﷯﷮𝑑𝑥﷯ + 𝑒﷮ 𝑥﷮4﷯﷯. 𝑑 𝑥﷮4﷯﷯﷮𝑑𝑥﷯ + 𝑒﷮ 𝑥﷮5﷯﷯. 𝑑 𝑥﷮5﷯﷯﷮𝑑𝑥﷯ = 𝒆﷮𝒙﷯ + 2x 𝒆﷮ 𝒙﷮𝟐﷯﷯ + 𝟑 𝒙﷮𝟐﷯ 𝒆﷮ 𝒙﷮𝟑﷯﷯ + 𝟒 𝒙﷮𝟑﷯ 𝒆﷮ 𝒙﷮𝟒﷯﷯ + 𝟓𝒙﷮𝟒 ﷯ 𝒆﷮ 𝒙﷮𝟓﷯﷯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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