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


Example 28 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 ๐’๐’๐’ˆโก๐’š = ๐’™ ๐’๐’๐’ˆโก ๐’‚ 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 = ๐’๐’๐’ˆโก๐’‚ (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‘ฆ/๐‘‘๐‘ฅ = ๐’‚^๐’™ ๐’๐’๐’ˆโก๐’‚

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