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

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

  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Serial order wise

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.