Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Question 24: 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): (ax 2 + sin x) (p + q cos x) Solution 24: Let f x ax 2 sin x (p + q cos x) By product rule, d d f ' x ax sin x p qcos x p qcos x ax sin x dx dx 2 2 2 ax sin x qsin x p qcos x2ax cos x 2 qsin x ax sin x p qcos x 2ax cos x Question 25: 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): (x + cos x) (x – tan x) Solution 25: Let f(x) = (x + cos x) (x – tan x) By product rule, d d f ' x (x + cos x) x tan xx tan x x cos x dx dx d d x + cos x x tan x x tan x1 sin x dx dx d x + cos x1 tan x x tan x1 sin x ... i dx Let g x tan x. Accordingly, g(x+h)=tan x+h By first principle, gx hg x g' x lim h0 h tan x htan x lim h0 h lim 1 sin( x h) sin x h0 h cos x h cos x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ 1 sin( x h)cos x sin xcos x h lim h0 h cos x hcos x 1 1 sin( x h x) lim cos x h0 h cos x h 1 1 sinh lim cos x h0 h cos x h 1 sinh 1 . lim . lim cos x h0 h h0 cos x h 1 1 .1. cos x cos x0 1 2 cos x 2 sec x ii x x 2 x x x x Therefore, from (i) and ii ,We obtain f' x cos (1 sec ) tan 1 sin 2 x cos x tan x x tan x1 sin x 2 tan x x cos x x tan x 1sin x Question 26: 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): Solution 26: Let f(x) = 4 x 5sin x 3x7cos x By quotient rule, f ' x d dx 4x5sin x 3x7cos x 3x 7cos x 4x 5sin x4x 5sin x 3x 7cos x 3x7cos x 2 d dx Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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