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



  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Concept wise


Example 31 Differentiate ๐‘Ž^๐‘ฅ ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ, where a is a positive constant. Let y = ๐‘Ž^๐‘ฅ Taking log on both sides logโก๐‘ฆ = logโก๐‘Ž^๐‘ฅ logโก๐‘ฆ = ๐‘ฅ logโก ๐‘Ž Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ (๐‘‘(logโก๐‘ฆ))/๐‘‘๐‘ฅ = ๐‘‘/๐‘‘๐‘ฅ(๐‘ฅ logโก๐‘Ž) (๐‘‘(logโก๐‘ฆ))/๐‘‘๐‘ฅ = logโก๐‘Ž (๐‘‘๐‘ฅ/๐‘‘๐‘ฅ) (๐‘‘(logโก๐‘ฆ))/๐‘‘๐‘ฅ = logโก๐‘Ž (๐‘™๐‘œ๐‘”โกใ€–๐‘Ž^๐‘=๐‘ ๐‘™๐‘œ๐‘”โก๐‘Ž ใ€—) (๐‘‘(logโก๐‘ฆ))/๐‘‘๐‘ฅ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฆ = logโก๐‘Ž (๐‘‘(logโก๐‘ฆ))/๐‘‘๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = logโก๐‘Ž 1/๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = logโก๐‘Ž ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘ฆ logโก๐‘Ž Putting back ๐‘ฆ = ๐‘Ž^๐‘ฅ ๐’…๐’š/๐’…๐’™ = ๐’‚^๐’™ ๐’๐’๐’ˆโก๐’‚

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.