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, 2 Differentiate the functions in, โ(((๐ฅ โ 1)(๐ฅ โ 2))/((๐ฅ โ 3)(๐ฅ โ 4)(๐ฅ โ 5))) Let ๐ฆ=โ(((๐ฅ โ 1)(๐ฅ โ 2))/((๐ฅ โ 3)(๐ฅ โ 4)(๐ฅ โ 5))) ๐ฆ= (((๐ฅ โ 1)(๐ฅ โ 2))/((๐ฅ โ 3)(๐ฅ โ 4)(๐ฅ โ 5)))^(1/2) Taking log both sides logโก๐ฆ = log (((๐ฅ โ 1)(๐ฅ โ 2))/((๐ฅ โ 3)(๐ฅ โ 4)(๐ฅ โ 5)))^(1/2) logโก๐ฆ = 1/2 log (((๐ฅ โ 1)(๐ฅ โ 2))/((๐ฅ โ 3)(๐ฅ โ 4)(๐ฅ โ 5))) (As ๐๐๐โก(๐^๐) = ๐ ๐๐๐โก๐) logโก๐ฆ = 1/2 [logโกใ((๐ฅโ1)(๐ฅโ2))โlogโก((๐ฅโ3)(๐ฅโ4)(๐ฅโ5)) ใ ] logโก๐ฆ = 1/2 . [("log " (๐ฅ+1)" + log " (๐ฅโ2))" โ " (logโก(๐ฅโ3)+logโกใ(๐ฅโ4)+logโก(๐ฅโ5) ใ )] logโก๐ฆ = 1/2 . ["log " (๐ฅ+1)" + log " (๐ฅ+2)" โ " logโก(๐ฅโ3)โlogโกใ(๐ฅโ4)โlogโก(๐ฅโ5) ใ ] Differentiating both sides ๐ค.๐.๐ก.๐ฅ. ๐(logโก๐ฆ)/๐๐ฅ = (๐ (1/2 " ." logโกใ(๐ฅ+1)" +" logโกใ (๐ฅ+2)" โ " logโก(๐ฅโ3)โlogโกใ(๐ฅโ4)โlogโก(๐ฅโ5) ใ ใ ใ ))/๐๐ฅ ๐(logโก๐ฆ)/๐๐ฅ (๐๐ฆ/๐๐ฆ) = 1/2 (๐(ใlog ใโกใ(๐ฅ + 1)" +" logโกใ(๐ฅ + 2)" โ " logโก(๐ฅ โ 3) โ logโกใ(๐ฅ โ 4) โ logโก(๐ฅ โ 5) ใ ใ ใ )/๐๐ฅ) 1/๐ฆ . ๐๐ฆ/๐๐ฅ = 1/2 (1/(๐ฅ + 1)+1/(๐ฅ + 2)โ1/(๐ฅ โ 3)โ1/(๐ฅ โ 4)โ1/(๐ฅ โ 5)) ๐๐ฆ/๐๐ฅ = 1/2 ๐ฆ(1/(๐ฅ โ 1)+1/(๐ฅ โ 2)โ1/(๐ฅ โ 3)โ1/(๐ฅ โ 4)โ1/(๐ฅ โ 5)) ๐ ๐/๐ ๐ = ๐/๐ โ(((๐ โ ๐)(๐ โ ๐))/((๐ โ ๐)(๐ โ ๐)(๐ โ ๐))) (๐/(๐ โ ๐)+๐/(๐ โ ๐)โ๐/(๐ โ ๐)โ๐/(๐ โ ๐)โ๐/(๐ โ ๐))
Ex 5.5
Ex 5.5, 2 You are here
Ex 5.5, 3 Important
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