Chapter 13 Class 11 Limits and Derivatives
Example 3 (i) Important
Ex 12.1, 6 Important
Ex 12.1,10 Important
Ex 12.1, 13
Ex 12.1, 16
Ex 12.1, 22 Important
Ex 12.1, 25 Important
Ex 12.1, 28 Important
Ex 12.1, 30 Important
Ex 12.1, 32 Important
Ex 12.2, 9 (i)
Ex 12.2, 11 (i)
Example 20 (i)
Example 21 (i)
Example 22 (i)
Misc 1 (i)
Misc 6 Important
Misc 9 Important
Misc 24 Important
Misc 27 Important
Misc 28 Important
Misc 30 Important You are here
Chapter 13 Class 11 Limits and Derivatives
Last updated at April 16, 2024 by Teachoo
Misc 30 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): đĽ/(đ đđđ đĽ) Let f(x) = đĽ/(đ đđđ đĽ) Let u = x & v = sinn x â´ f(x) = đ˘/đŁ So, fâ(x) = (đ˘/đŁ)^ⲠUsing quotient rule fâ(x) = (đ˘^ⲠđŁ âă đŁă^Ⲡđ˘)/đŁ^2 Finding uâ & vâ u = x uâ = 1 Now, v = sinn x Let p = sin x v = pn By Leibnitz product rule vâ = (pn)â pâ = n pn â 1 pâ Putting p = sin x = n sinn â 1 x (sin x)â = n sinn â 1 x cos x Now, fâ(x) = (đ˘/đŁ)^Ⲡ= (đ˘^ⲠđŁ âă đŁă^Ⲡđ˘)/đŁ^2 = ( 1 (sinđâĄă đĽă ) â ăđ đ đđă^(đâ1) đĽ cosâĄăđĽ (đĽ)ă)/ăă(đ đđă^đ đĽ)ă^2 = ( ăđ đđă^đ đĽ â đĽ (đăđ đđă^(đâ1) đĽ cosâĄăđĽ) ă)/ăă(đ đđă^đ đĽ)ă^2 = ( ăđđđă^(đâđ) đ . sinâĄăđĽ â đĽ (đ ă ăđ đđă^(đâ1) đĽ cosâĄăđĽ) ă)/ăă(đ đđă^đ đĽ)ă^2 = ( ăđđđă^(đâđ) đ ă(sinăâĄăđĽ â đđĽ . ă cosâĄăđĽ) ă)/(ăđ đđă^2đ đĽ) = sinâĄăđĽ â đđĽ cosâĄđĽ ă/(ăđ đđă^2đ đ . ăđđđă^(â(đâđ) ) đ) = sinâĄăđĽ â đđĽ cosâĄđĽ ă/(ăđđđă^((đđ â đ+đ)) đ) = sinâĄăđĽ â đđĽ cosâĄđĽ ă/(ăđ đđă^(đ + 1) đĽ) Thus, fâ(x) = đđđâĄăđ â đđ đđđâĄđ ă/(ăđđđă^(đ + đ) đ)