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CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 13 –

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Question 21: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s sin xa are fixed non-zero constants and m and n are integers): cos x Solution 21: sin xa Let f(x) = cos x By quotient rule, d d cos x sin x a sin x a cos x ' dx f x dx 2 cos x d cos x sin x a sin x a sin x f ' x dx ... i 2 cos x Let g(x)=sin (x + a). Accordingly, g(x + h) = sin (x + h + a) By first principle, g( x h) g x g' x lim h0 h 1 lim sin x h a sin x a h0 h 1 x h a x a x h a x a lim 2cos sin h0 h 2 2 lim 1 2cos 2x 2a h sin h h0 h h 2 h sin 2x 2a h 2 lim cos h0 h h 2 sin h 2x 2a h 2 h limcos .lim As h 0 0 h0 h h 0 h 2 2 2 2x 2a sinh cos 1 lim 1 2 h0 h cos x a ... ii From (i) and (ii), we obtain 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 ______________________________________________________________________________ sin sin cos x.cos x a x x a f ' x 2 cos x cos x a x 2 cos x cos a 2 cos x Question 22: 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 4 (5 sin x - 3 cos x) Solution 22: 4 Let f ( x) x (5sin x 3cos x) By product rule, 4 d d 4 f '( x) x (5sin x 3cos x) (5sin x 3cos x) x dx dx d d d x 5 sin x 3 cos x (5sin x 3cos x) x dx dx dx 4 3 x 5cos x 3sin x (5sin x 3cos x) 4x 3 x 5xcos x 3xsin x 20sin x 12cos x 4 4 Question 23: 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 2 + 1) cos x Solution 23: Let f(x) = x 2 1 cos x By product rule, 2 d d 2 f ' x x 1 cos x cos x x 1 dx dx 2 x 1 sin x cos x 2x 2 x sin x sin x 2xcos x 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 9 - Sequences and

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    Class XI Chapter 11 - Conic Section

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    Class XI Chapter 12 - Introduction

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