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
Misc 5 Differentiate ๐ค.๐.๐ก. ๐ฅ the function, (ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2)/โ(2๐ฅ+7 ) , โ 2 < ๐ฅ < 2 Let ๐ฆ= (ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2)/โ(2๐ฅ+7 ) Differentiating both sides ๐ค.๐.๐ก.๐ฅ. ๐๐ฆ/๐๐ฅ = ๐/๐๐ฅ ((ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2)/โ(2๐ฅ+7 )) Using quotient rule As (๐ข/๐ฃ)^โฒ = (๐ข^โฒ ๐ฃ โ ๐ฃ^โฒ ๐ข)/๐ฃ^2 where u = cosโ1 ๐ฅ/2 & v = โ(2๐ฅ+7) ๐๐ฆ/๐๐ฅ = (๐(ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2)/๐๐ฅ . โ(2๐ฅ + 7 ) โ ๐(โ(2๐ฅ + 7 ))/๐๐ฅ . ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 )/(โ(2๐ฅ+7 ))^2 ๐๐ฆ/๐๐ฅ = ((โ1)/โ(1 โ(๐ฅ/2)^2 ) . ๐/๐๐ฅ (๐ฅ/2) โ(2๐ฅ + 7 ) โ 1/(2โ(2๐ฅ + 7)) . ๐(2๐ฅ + 7)/๐๐ฅ . ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 )/(โ(2๐ฅ + 7 ))^2 ๐๐ฆ/๐๐ฅ = ((โ1)/โ(ใ(4 โ ๐ฅ)/4ใ^2 ) . 1/2 โ(2๐ฅ + 7 ) โ 1/(2โ(2๐ฅ + 7)) . (2 + 0) . ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 )/((2๐ฅ + 7) ) ๐๐ฆ/๐๐ฅ = ((โ2)/โ(ใ4 โ ๐ฅใ^2 ) . 1/2 โ(2๐ฅ + 7 ) โ 1/(2โ(2๐ฅ + 7)) . 2 . ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 )/((2๐ฅ + 7) ) ๐๐ฆ/๐๐ฅ = ((โ โ(2๐ฅ + 7 ))/( โ(ใ4 โ ๐ฅใ^2 )) โ (. ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2)/โ(2๐ฅ + 7) )/((2๐ฅ + 7) ) ๐๐ฆ/๐๐ฅ = (โ โ(2๐ฅ + 7 ) ( โ(2๐ฅ + 7 )) โ ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 โ(ใ4 โ ๐ฅใ^2 ))/((2๐ฅ + 7) (โ(2๐ฅ + 7 )) (โ(ใ4 โ ๐ฅใ^2 )) ) ๐๐ฆ/๐๐ฅ = ใโ(โ(2๐ฅ + 7 ))ใ^2/((2๐ฅ + 7) ( โ(2๐ฅ + 7 )) (โ(ใ4 โ ๐ฅใ^2 )) ) "+ " (ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 โ(ใ4 โ ๐ฅใ^2 ))/((2๐ฅ + 7) ( โ(2๐ฅ + 7 )) (โ(ใ4 โ ๐ฅใ^2 )) ) ๐๐ฆ/๐๐ฅ = (โ(2๐ฅ + 7))/((2๐ฅ + 7) โ(2๐ฅ + 7 ) โ(ใ4 โ ๐ฅใ^2 )) "+ " (ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 )/((2๐ฅ+7) โ(2๐ฅ + 7 ) ) ๐๐ฆ/๐๐ฅ = (โ1)/(โ(2๐ฅ + 7 ) โ(ใ4 โ ๐ฅใ^2 )) "+ " (ใ๐๐๐ ใ^(โ1 ) ๐ฅ/2 )/((2๐ฅ+7) (2๐ฅ + 7)^(1/2) ) ๐ ๐/๐ ๐ = (โ๐)/(โ(๐๐ + ๐) โ(ใ๐ โ ๐ใ^๐ ))โ(ใ๐๐๐ใ^(โ๐ ) ๐/๐ )/((๐๐ + ๐)^(๐/๐) )
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)
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 You are here
Misc 4
Misc 13 Important
About the Author