Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ f ' x 1tan sec 1 tan x 2 x x x 2 Question 29: 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 + sec x) (x - tan x) Solution 29: Let f(x) = (x + sec x) (x – tan x) By product rule, d d f x ( x sec x) x tan xx tan x x sec x dx dx d d d d ( x sec x) x tan x x tan x x sec x dx dx dx dx d d ( xsec x) 1 tan x xtan x 1 sec x i dx dx Let f x tan x, f x sec x 1 2 Accordingly, f x h tan x h and f x h sec x h 1 2 f1 x h f1 x f ' 1 x lim h0 h tan x htan x lim h0 h sin x h sin x lim h0 cos x h cos x 1 sin x hcos x sin xcos xx h lim h0 h cos x hcos x lim 1 sin x hx h0 h cos x h cos x lim 1 sinh h0 h cos x h cos x sinh 1 lim . lim h0 h h0 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 2 1 sec x 2 cos x d dx f2x h f2x f ' 2 x lim h0 h sec x hsec x lim h0 h lim 1 1 1 h0 h cos( x h ) cos x 2 1 tan x sec x ... ii 1 cos x cos x h lim h0 h cos x h cos x 2sin x x h .sin x x h 1 1 2 2 .lim cos x h0 h cos x h 2 2sin x h .sin h 1 1 2 2 .lim cos x h0 h cos x h h sin 2x h 2 sin 2 h 1 1 2 .lim cos x h0 h cos x h h sin 2x h 2 limsin lim h0 2 h 0 h 2 2 sec x. limcos x h sin x.1 sec x. cos. x h0 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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