Misc 4 - Find derivative: (ax + b) (cx + d)2 - Class 11 Limits - Derivatives by formula - x^n formula

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  1. Chapter 13 Class 11 Limits and Derivatives
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Misc 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 non-zero constants and m and n are integers): (ax + b) (cx + d)2 Let f(x) = (ax + b) (cx + d)2 Let u = ax + b & v = (cx + d)2 So, f(x) = uv f (x) = (uv) = u v + v u Finding u & v u = ax + b u = a . 1x1 1 + 0 = ax0 = a v = (cx + d)2 v = c2 x2 + d2 + 2cdx v = 2c2 . x2 1 + 0 + 2cd. 1 .x1 1 = 2c2 x + 2cdx0 = 2c2x + 2cd Now, f (x) = (uv) = uv + v u = a(cx + d)2 + ( 2c2x + 2cd) (ax + b) = a (cx + d)2 + 2c (cx + d) (ax + b) = 2c (cx + d) (ax + b) + a (cx + d)2 Hence f (x) = 2c (cx + d) (ax + b) + a (cx + d)2

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.