Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ d d d d 3x 7cos x 4 x 5 sin x 4x 5sin x 3 x 7 cos x dx dx dx dx 3x7cos x 2 3x 7cos x4x 5cos x4x 5sin x37sin x 2 3x7cos x 12 15 cos 28cos 35cos 12 28 sin 15sin 35 cos sin 2 3x7cos x 2 2 2 x x x x x x x x x x x 2 2 15x cos x 28cos x 28xsin x 15sin x 35(cos x sin x) 2 3x7cos x 35 15xcos x 28cos x 28xsin x 15sin x 3x 7cos x 2 Question 27: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s x 2 cos 4 are fixed nonzero constants and m and n are integers): sin x Solution 27: x 2 cos 4 Let f(x) = sin x By quotient rule, d 2 2 d sin x x x sin x ' cos . dx dx f x 2 4 sin x 2 sin x.2x x cos x cos . 2 4 sin x xcos 2sin x xcos x 4 2 sin 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 ______________________________________________________________________________ Question 28: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s x are fixed non-zero constants and m and n are integers): 1 tan x Solution 28: x Let f(x) = 1 tan x f ' x d d dx dx 2 1 tan x 1 tan x x x 1 tan x d 1 tan x x 1 tan x dx 2 1 tan x x f ' x ... i Let g x 1 tan .Accordingly, g(x+h)=1+tan x+h . By first principle, gx hgx g' x lim h0 h 1 tan x h1 tan x lim h 0 h lim 1 sin x h sin x h0 h 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 h x h0 h cos x h cos x lim 1 sinh h0 h cos x h cos x lim sinh . lim 1 h0 h h0 cos x h cos x 1 2 1 sec x 2 cos x d dx From (i) and (ii), we obtain 2 1 tan x sec x ... ii Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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