Misc 25 - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Miscellaneous
Misc 1 (i)
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Transcript
Misc 25 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): (x + cos x) (x tan x) Let f (x) = (x + cos x) (x tan x) Let u = x + cos x & v = x tan x f(x) = uv So, f (x) = Using product rule f (x) = + Finding u & v u = x + cos x u = (x + cos x) = 1 sin x & v = x tan x v = (x tan x) = 1 sec2 x Now, f (x) = = + = (1 sin x) (x tan x) + (1 sec2 x) (x + cos x) = (1 sin x) (x tan x) (sec2 x 1) (x +cos x) = (1 sin x) (x tan x) tan2x (x + cos x) = tan2x (x + cos x) + (x tan x) (1 sin x)
