Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ pr qr pr ps 2 x x x qr ps 2 x Question 4: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax + b) (cx + d) 2 Solution 4: Let f ' x ax b cx d 2 By Leibnitz product rule, d 2 2 d f ' x ax b cx d cx d ax b dx dx d 2 2 2 2 d ax b c x 2cdx d cx d ax b dx dx d 2 2 d d 2 2 d d ax b c x 2cdx d cx d ax b dx dx dx dx dx 2 2 2 ax b c x cd cx d a 2c ax b cx d a cx d 2 2 Question 5: 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): Solution 5: Let f(x) = ax b cx d By quotient rule, d f ' dx x ax b cx d cx d ax bax b cx d cx d 2 d dx 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 ______________________________________________________________________________ cx daax dc 2 cx d acx ad acx bc 2 cx d ad bc cx d 2 Question 6: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s 1 1 are fixed nonzero constants and m and n are integers): x 1 1 x Solution 6: 1 x 1 1 1 Let x x x f x ,where x 0 1 x 1 1 x 1 x x By quotient rule, d d x 1 x 1 x 1 x 1 f ' x dx dx , x 0,1 2 x-1 x**11** x**11** 2 x-1 = , x 0,1 x1 x1 2 , x 0,1 x-1 2 = , x 0,1 2 x-1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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