![Misc 15 - Chapter 13 Class 11 Limits and Derivatives - Part 2](https://d1avenlh0i1xmr.cloudfront.net/f22da84f-babf-482a-b9c8-dc70f57adc44/slide47.jpg)
Miscellaneous
Last updated at April 16, 2024 by Teachoo
Misc 15 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): cosec x cot x Let f(x) = cosec x cot x Let u = cosec x & v = cot x So, f(x) = uv f (x) = (uv) Using product rule f (x) = u v + v u Finding u & v u = cosec x u = cosec x cot x v = cot x v = cosec2x Now, f (x) = (uv) = u v + v u = cosec x cot x (cot x) + ( cosec2x) (cosec x) = cosec x . cot2 x cosec3x = cosec3x cosec x cot2x