# Example 22 (ii) - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)

Last updated at Sept. 6, 2021 by Teachoo

Examples

Example 1 (i)

Example 1 (ii)

Example 1 (iii)

Example 2 (i)

Example 2 (ii) Important

Example 2 (iii) Important

Example 2 (iv)

Example 2 (v)

Example 3 (i) Important

Example 3 (ii) Important

Example 4 (i)

Example 4 (ii) Important

Example 5

Example 6

Example 7 Important

Example 8

Example 9

Example 10 Important

Example 11

Example 12

Example 13 Important

Example 14

Example 15 Important

Example 16

Example 17 Important

Example 18

Example 19 (i) Important

Example 19 (ii)

Example 20 (i)

Example 20 (ii) Important

Example 21 (i)

Example 21 (ii) Important

Example 22 (i)

Example 22 (ii) Important You are here

Last updated at Sept. 6, 2021 by Teachoo

Example 22 Find the derivative of (ii) (π₯ + πππ β‘π₯)/π‘ππβ‘π₯ Let f(x) = (π₯ + πππ β‘π₯)/π‘ππβ‘π₯ Let u = x + cos x & v = tan x β΄ f(x) = π’/π£ So, fβ(x) = (π’/π£)^β² Using quotient rule fβ(x) = (π’^β² π£ βγ π£γ^β² π’)/π£^2 Finding uβ & vβ u = x + cos x uβ = (x + cos x)β = 1 β sin x v = tan x vβ = sec2x Now, fβ(x) = (π’^β² π£ βγ π£γ^β² π’)/π£^2 = ((π βγ π¬π’π§γβ‘γπ) (πππ§β‘γπ) β πππππ (π + γ ππ¨π¬γβ‘γπ)γ γ γ)/γ(πππ§β‘γπ)γγ^π (xn)β = n xn β 1 Derivative of cos x = βsin x Derivative of tan x = sec2x (Calculated in Example 17)