Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ x h cos x cos lim h0 h cos xcosh sin xsinhcos x lim h0 h cos x1 cosh sin xsinh lim h 0 h cos x(1 cosh sin xsinh lim h0 h h 1cosh sinh cos xlim sin xlim h0 h h0 h 1cosh cos x0sin x1 lim 0 h0 h sin x f '( x) sin x and sinh lim 1 h0 h Question **11**: Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x (iv) cosec x (v) 3cot x + 5cosec x (vi) 5sin x - 6cos x + 7 (vii) 2tan x - 7sec x Solution **11**: (i) Let f (x) = sin x cos x. Accordingly, from the first principle, f x h f x f ' x lim h0 h sin x hcos x hsin xcos x lim h0 h 1 lim 2sin( x h)cos x h2sin xcos x h0 2h 1 lim sin2 x h sin2x h0 2h 1 2x 2h 2x 2x 2h2x lim 2cos .sin h0 2h 2 2 1 4x2h 2h lim cos .sin h0 2h 2 2 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 lim cos 2x hsinh h0 2h sinh limcos 2 xh.lim h0 h0 h cos 2x 0 .1 cos2x (ii) Let f (x) = sec x. Accordingly, from the first principle, f x h f x f ' x lim h0 h sec x hsec x lim h0 h lim 1 1 1 h0 h cos( x h ) cos x 1 cos x cos x h lim h0 h cos xcos x h x x h x x h 2sin sin 1 1 2 2 .lim cos x h0 h cos( x h) 2x h 2sin 1 1 sin h 2 .lim 2 cos x h0 h cos( x h) h sin 2x h 2 sin 2 h 1 1 2 .lim cos x h0 2h cos( x h) 2 sin h sin x h 1 2 2 .lim .lim cos x h0 h h0 cos( x h) 2 1 sin x .1. cos x cos x sec xtan x (iii) Let f (x) = 5 sec x + 4 cos x. Accordingly, from the first principle, Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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