Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ By Leibnitz product rule, 3 d d 3 f '( x) 5x + 3x-1 x 1 x 1 5x + 3x-1 dx dx 3 2 5x + 3x-1 1 x 1 5.3x + 3-0 3 2 5x + 3x-1 x **11**5 x 3 3 3 2 5x + 3x-1+15x 3x 15x 3 3 2 20x 15x 6x 4 (iii) Let f (x) = x â €’’3 (5 + 3x) By Leibnitz product rule, d d f'(x)=x 5 + 3x 5 3x x dx dx -3 -3 x x =x 0 + 3 5 3 3x -3 -3-1 x 3 53 3x -3 -4 3x 15x 9x -3 -4 -3 -3 -4 6x 15x -3 5 3x 2 x -3 3x 2x 5 x 3 4 5 2 x x (iv) Let f (x) = x 5 (3 â€“ 6 x a €’’9 ) By Leibnitz product rule, d d f '( x) x 3 -6x 36x x dx dx 5 -9-1 -9 4 x 06 9 x 36x 5x 5 -9 9 5 x 54x 15x 30x 5 -10 4 -5 54x 15x 30x -5 4 -5 -5 4 24x 15x -5 24 24x 5 x a (v) Let f (x) = x €’’4 (3 â€“ 4 x a €’’5 ) By Leibnitz product rule, 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 ______________________________________________________________________________ d d f '( x) x 3 -4x 3 4x x -4 -5 5 -4 dx dx x x 04 5 x 34x 4 -4 -5-1 -5 4 1 x 20x 34x 4x -4 -6 -5 -5 20x 12x 16x -10 -5 -10 -10 -5 36x 12x 12 36 -5 10 x x 2 2 x (vi) Let f (x) = x1 3x1 f’(x) = d 2 2 d x dx x 1 dx 3x 1 By quotient rule, d d d 2 2 d x 1 2 2 x 1 3x 1 x x 3x 1 ' dx dx dx dx f x 2 2 x1 3x1 2 x 10 21 3x 12x x 3 2 2 x1 3x1 2 2 2 6x 2x 3x 2 2 x1 3x1 2 2 2 3x 2x 2 2 x1 3x1 2 x3x 2 2 2 x1 3x1 Question 10: Find the derivative of cos x from first principle. Solution 10: Let f (x) = cos x. Accordingly, from the first principle, f xh f x f ' x lim h 0 h 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 15 - Statistics Ma

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