Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ 1sin x h cos x sin xcos x h 1cos x cos x h 2lim 7lim h0h cos xcos x h h0h cos xcos( x h) x x h x x h 2sin sin 1 sin x hx 1 2 2 2lim 7lim h0h cos xcos x h h0 h cos xcos( x h 2x h h 2sin sin sinh 1 1 2 2 2 lim 7lim h0 h cos xcos x h h0 h cos xcos x h h 2 sin sin x h sinh 1 2 2 lim lim 7 lim 2 lim h0 h h0 cos xcos x h h0 h h0 cos xcos x h 2 1 sin x 2.1. 7.1 cos xcos x cos xcos x 2 2sec x 7sec xtan x Miscellaneous Exercise Question 1: Find the derivative of the following functions from first principle: (i) â€“x (ii) (â€“x)â €’’1 (iii) sin (x + 1) (iv) cos 8 Solution 1: (i) Let f(x) = â€“x. Accordingly, f(x + h) = - (x + h) By first principle, f x h f x f ' x lim h0 h x hx lim h0 h x h x lim h0 h h lim h0 h 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 ______________________________________________________________________________ h0 lim 1 1 1 1 1 x x x h 1 iiLet f x x . Accordingly, f x+h By first principle, f x h f x f ' x lim h0 h 1 1 1 lim h0 h x h x 1 1 1 lim h0 h x h x 1 x x h lim h0 h xx h 1 x x h lim h0 h xx h 1 h lim h0 h x x h 1 lim h0 x x h 1 1 2 x. x x (iii) Let f(x) = sin (x + 1). Accordingly, f x+h sin x h1 By first principle, f x h f x f ' x lim h0 h 1 lim sin x h 1 sin x 1 h0 h 1 x h1 x 1 x h1 x 1 lim 2cos sin h0 h 2 2 1 2xh2 h lim 2cos sin h0 h 2 2 sin h 2xh2 2 lim cos . h0 2 h 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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