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

Last updated at Jan. 16, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
Transcript
Find the derivative of f given by f (x) = sec–1 𝑥 assuming it exists. Let 𝑦 = sec^(–1) 𝑥 𝑠𝑒𝑐𝑦= 𝑥 𝑥 =𝑠𝑒𝑐𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑥/𝑑𝑥 = (𝑑 (𝑠𝑒𝑐𝑦 ))/𝑑𝑥 1 = (𝑑 (𝑠𝑒𝑐𝑦 ))/𝑑𝑥 We need 𝑑𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (sec𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = tan𝑦 .sec𝑦 . 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 tan𝑦 .sec𝑦= 1 𝑑𝑦/𝑑𝑥 = 1/(𝒕𝒂𝒏𝒚 .〖 sec〗𝑦 ) 𝑑𝑦/𝑑𝑥 = 1/((√(〖𝐬𝐞𝐜〗^𝟐𝒚 − 𝟏)) .〖 sec〗𝑦 ) Putting value of 𝑠𝑒𝑐𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = 1/((√(𝑥^2 − 1 ) ) . 𝑥) 𝑑𝑦/𝑑𝑥 = 1/(𝑥 √(𝑥^2 − 1 ) ) As 𝑦 = sec^(−1) 𝑥 So, 𝑠𝑒𝑐𝑦 = 𝑥 Hence 𝒅(〖𝒔𝒆𝒄〗^(–𝟏) 𝒙)/𝒅𝒙 = 𝟏/(𝒙 √(𝒙^𝟐 − 𝟏 ) ) As tan2 θ = sec2 θ – 1, tan θ = √("sec2 θ – 1" )
Finding derivative of Inverse trigonometric functions
Example 26 Important
Example 27
Derivative of cot-1 x (cot inverse x)
Derivative of sec-1 x (Sec inverse x) You are here
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
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