Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ 2 f x x a b x ab d 2 f ' x x a b x ab dx d 2 d d x a b x ab dx dx dx d n n 1 On using theorem x nx ,we obtain dx f ' x 2x a b 0 2x a b 2 ( ii)Let f x ax b f x a x 2abx b 2 4 2 2 2 d d d d f ' x a x 2abx b a x 2ab x b dx dx dx dx d n n 1 On using theorem x nx ,we obtain dx 2 4 2 2 2 4 2 2 2 3 2 f'(x)= a 4x 2ab 2x b 0 2 3 4a x 4 4ax ax Let f () x 2 abx b xa xb d x a f ' x dx x b By quotient rule, d x b x ax a x b dx dx xb 2 x b1 x a1 2 xb f' x x b x a 2 xb ab xb 2 d 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 8: Find the derivative of Solution 8: n x a xa n for some constant a. n n x a Let f(x) = xa n n d x a f '( x) dx x a By quotient rule, d n n n n d x a x a x a x a f ' x dx dx 2 xa n1 n n x anx 0x a xa nx anx x a 2 xa n n1 n n 2 Question 9: Find the derivative of 3 (i) 2x (ii) (5x 3 + 3x â€“ 1) (x â€“ 1) 4 â (iii) x €’’3 (5 + 3x) (iv) x5 (3 â€“6 x a €’’9 ) 2 2 x (v) xâ€“4 (3 â€“ 4xâ€“5) (vi) x1 3x1 Solution 9: 3 (i) Let f(x) = 2x 4 d 3 f '( x) 2x dx 4 d d 3 = 2 x dx dx 4 =2-0 =2 (ii) Let f (x) = (5x 3 + 3x â€“ 1) (x â€“ 1) Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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