Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ sin h 1 2x h2 1 2 h lim cos .lim [ As h 0 0] h0 h 2 h 0 h h 2 2 2 2x02 sin x cos .1 lim 1 2 h0 x cos x 1 (iv) Let f x =cos x- . Accordingly, f x+h cos x h 8 8 By first principle, f x h f x f ' x lim h0 h 1 lim cos x h cos x h0 h 8 8 x h x 1 x h x 8 8 lim 2sin sin 8 8 h0 h 2 2 1 2x h lim 2sin 4 h sin h0 h 2 2 h 2x h sin 4 2 lim sin h0 2 h 2 h 2x h sin 4 2 h lim sin .lim As h 0 0 h0 2 h0 h 2 2 2x 0 sin 4 .1 2 sin x 8 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 2: 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 + a) Solution 2: Let f(x) = x + a. Accordingly, f(x + h) = x + h + a By first principle, f x h f x f ' x lim h0 h x h a x a lim h0 h h lim h0 h lim 1 1 h0 Question 3: 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): px q r s x Solution 3: Let f(x) = px q r s x By Leibnitz product rule, r r f ' x px q s s px q x x 1 r px qrx s s p x 2 r px qrx s p x r r px q s p 2 x x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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