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Last updated at April 26, 2021 by Teachoo
Transcript
Derivative of ใ๐๐๐ใ^(โ๐) ๐ ๐ (๐ฅ)=ใ๐๐๐กใ^(โ1) ๐ฅ Let ๐= ใ๐๐๐ใ^(โ๐) ๐ cotโกใ๐ฆ=๐ฅใ ๐=๐๐จ๐ญโกใ๐ ใ Differentiating both sides ๐ค.๐.๐ก.๐ฅ ๐๐ฅ/๐๐ฅ = (๐ (cotโก๐ฆ ))/๐๐ฅ 1 = (๐ (cotโก๐ฆ ))/๐๐ฅ ร ๐๐ฆ/๐๐ฆ 1 = (๐ (cotโก๐ฆ ))/๐๐ฆ ร ๐๐ฆ/๐๐ฅ 1 = โ๐๐จใ๐ฌ๐๐ใ^๐ ๐ . ๐๐ฆ/๐๐ฅ 1 = โ(๐ +๐๐๐๐๐) ๐๐ฆ/๐๐ฅ ๐๐ฆ/๐๐ฅ = (โ1)/(1 + ใ๐๐จ๐ญใ^๐โก๐ ) Putting ๐๐๐กโก๐ฆ = ๐ฅ ๐๐ฆ/๐๐ฅ = (โ1)/(๐^๐ + ๐) Hence (๐ (ใ๐๐จ๐ญใ^(โ๐)โกใ๐)ใ)/๐ ๐ = (โ๐)/(๐^๐ + ๐) (๐ด๐ ใ ๐๐๐ ๐๐ใ^2โกใ๐ฆ= ใ1+ใโกใ๐๐๐กใ^2โก๐ฆ ใ) As ๐ฆ = ใ๐๐๐กใ^(โ1) ๐ฅ So, ๐๐๐โก๐ = ๐
Finding derivative of Inverse trigonometric functions
Example 26 Important
Example 27
Derivative of cot-1 x (cot inverse x) You are here
Derivative of sec-1 x (Sec inverse x)
Derivative of cosec-1 x (Cosec inverse x)
Ex 5.3, 14
Ex 5.3, 9 Important
Ex 5.3, 13 Important
Ex 5.3, 12 Important
Ex 5.3, 11 Important
Ex 5.3, 10 Important
Ex 5.3, 15 Important
Misc 5 Important
Misc 4
Misc 13 Important
Finding derivative of Inverse trigonometric functions
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