Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Miscellaneous

Misc 1 (i)

Misc 1 (ii) Important

Misc 1 (iii)

Misc 1 (iv) Important

Misc 2

Misc 3 Important

Misc 4 Important

Misc 5

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11

Misc 12 Important

Misc 13

Misc 14 Important

Misc 15

Misc 16

Misc 17 Important

Misc 18 Important

Misc 19

Misc 20 Important

Misc 21

Misc 22 Important

Misc 23

Misc 24 Important

Misc 25

Misc 26

Misc 27 Important

Misc 28 Important

Misc 29 Important

Misc 30 Important You are here

Last updated at May 29, 2023 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)^â˛ Using quotient rule fâ(x) = (đ˘^â˛ đŁ âă đŁă^â˛ đ˘)/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)^â˛ = (đ˘^â˛ đŁ âă đŁă^â˛ đ˘)/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)