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 5.3, 15 Find ๐๐ฆ/๐๐ฅ in, y = secโ1 (1/( 2๐ฅ2โ1 )), 0 < x < 1/โ2 y = secโ1 (1/( 2๐ฅ^2 โ 1 )) ๐๐๐โก๐ = 1/(2๐ฅ^2 โ 1) ๐/๐๐จ๐ฌโก๐ = 1/(2๐ฅ^2 โ 1) cosโก๐ฆ = 2๐ฅ2โ1 y = cos โ1 (2๐ฅ2โ1) Putting ๐ฅ = cosโกฮธ ๐ฆ = cos โ1 (2๐๐๐ 2๐โ1) ๐ฆ = cos โ1 (cosโก2 ๐) ๐ฆ = 2๐ Putting value of ฮธ = cosโ1 x ๐ฆ = 2 ใ๐๐๐ ใ^(โ1) ๐ฅ Differentiating both sides ๐ค.๐.๐ก.๐ฅ . (๐(๐ฆ))/๐๐ฅ = (๐ (2ใ๐๐๐ ใ^(โ1) ๐ฅ" " ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 2 (๐ (ใ๐๐๐ ใ^(โ1) ๐ฅ" " ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 2 . ((โ1)/โ(1 โ ๐ฅ^2 )) ๐ ๐/๐ ๐ = (โ๐)/โ(๐ โ ๐^๐ ) (๐๐๐ โก2๐ " = 2 " ใ๐๐๐ ใ^2 ๐โ1) ((ใ๐๐๐ ใ^(โ1) ๐ฅ")โ = " (โ1)/โ(1 โ ๐ฅ^2 ))
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