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Misc 13 - Find derivative: (ax + b)n (cx + d)n - Class 11 - Miscellaneous

Misc 13 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Misc 13 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)n (cx + d)m Let f(x) = (ax + b)n (cx + d)m Let u = (ax + b)n & v = (cx + d)m f(x) = uv So, f (x) = (uv) f (x) = u v + v u Finding u & v u = (ax + b)n u = an (ax + b)n 1 v = (cx + d)m v = cm (cx + d)m 1 f (x) = (uv) = u v + v u = an (ax + b)n 1(cx + d)m + cm(cx + d)m 1 (ax + b)n = an (ax + b)n 1(cx + d)m 1 (cx + d) + cm (cx + d)m 1(ax + b)n 1 (ax + b) = (ax + b)n 1(cx + b)m 1 (an (cx + d)+ cm (ax + b)) = (ax + b)n 1(cx + b)m 1 (an (cx + d)+ mc (ax + b))

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.