Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ lim h0 m cx ch d cx d h m m m 1 ch cx d lim 1 1 h0 h cx d m 2 2 1 m mch mm 1 ch cx d lim 1 ... 1 h0 2 h cx d 2 cx d 2 2 m 1 mch mm1 c h cx d lim ... 2 Terms containing higher degree oh h h0 h cx d 2cx d 2 2 m mc mm1 c h cx d lim ... h0 2 cx d 2cx d m mch cx d 0 cx d mc cx d cx d mc cx d m m1 d m m1 cx d mc cx d ... 2 dx d Similarly, ax b na ax b ... 3 dx n n1 Therefore, from (1), (2), and (3), we obtain n m 1 m n1 f ' x ax b mc cx d cx d na ax b n1 m1 ax b cx d mc ax b nacx d Question 14: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): sin (x + a) Solution 14: Let, f x sin( x a) sin f x h x h a 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 ______________________________________________________________________________ By first principle, f x h f x f ' x lim h0 h sin x h asin x a lim h0 h 1 x h a x a x h a x a lim 2cos sin h0 h 2 2 1 2x 2a h h lim 2cos sin h0 h 2 2 h 2x 2a h sin lim cos 2 h0 2 h 2 h 2 2 sin x a h limcos lim 2 h Ash 0 0 h0 2 h 0 h 2 2 2 2x 2a sin x cos 1 lim 1 2 x0 x cos xa Question 15: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): cosec x cot x Solution 15: Let f(x) = cosec x cot x By Leibnitz product rule, f’(x) = cosec x(cot x)’+cot x(cosec x)’ ….(1) Let f1(x) = cot x. Accordingly, f1 (x + h) = cot (x + h) By first principle, Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 11 - Conic Section

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Class XI Chapter 12 - Introduction

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