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


Last updated at Jan. 3, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
Transcript
Ex 5.5, 15 Find ๐๐ฆ/๐๐ฅ of the functions in, ๐ฅ๐ฆ= ๐^((๐ฅ โ๐ฆ)) Given ๐ฅ๐ฆ= ๐^((๐ฅ โ๐ฆ)) Taking log both sides log (๐ฅ๐ฆ) = log ๐^((๐ฅ โ๐ฆ)) log (๐ฅ๐ฆ) = (๐ฅ โ๐ฆ) log ๐ log ๐ฅ+logโก๐ฆ = (๐ฅ โ๐ฆ) (1) log ๐ฅ+logโก๐ฆ = (๐ฅ โ๐ฆ) (As ๐๐๐โก(๐^๐ )=๐ . ๐๐๐โก๐) ("As " ๐๐๐โก๐=1) Differentiating both sides ๐ค.๐.๐ก.๐ฅ. ๐(log ๐ฅ + logโก๐ฆ )/๐๐ฅ = (๐(๐ฅ โ ๐ฆ))/๐๐ฅ ๐(log ๐ฅ)/๐๐ฅ + ๐(logโก๐ฆ )/๐๐ฅ = ๐(๐ฅ)/๐๐ฅ โ ๐(๐ฆ)/๐๐ฅ 1/๐ฅ + ๐(logโก๐ฆ )/๐๐ฅ . ๐๐ฆ/๐๐ฆ = 1 โ ๐๐ฆ/๐๐ฅ 1/๐ฅ + ๐(logโก๐ฆ )/๐๐ฆ . ๐๐ฆ/๐๐ฅ = 1 โ ๐๐ฆ/๐๐ฅ 1/๐ฅ + 1/๐ฆ . ๐๐ฆ/๐๐ฅ = 1 โ ๐๐ฆ/๐๐ฅ 1/๐ฆ . ๐๐ฆ/๐๐ฅ + ๐๐ฆ/๐๐ฅ = 1 โ 1/๐ฅ ๐๐ฆ/๐๐ฅ (1/๐ฆ +1) = ("1 โ " 1/๐ฅ) ๐๐ฆ/๐๐ฅ ((1 + ๐ฆ)/๐ฆ) = ((๐ฅ โ 1)/๐ฅ) ๐๐ฆ/๐๐ฅ = ((๐ฅ โ 1)/๐ฆ) . (๐ฆ/(1 + ๐ฆ)) ๐ ๐/๐ ๐ = ๐(๐ โ ๐)/๐(๐ + ๐)
Ex 5.5
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Ex 5.5, 15 You are here
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