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Miscellaneous (Term 1 and Term 2)
Last updated at May 29, 2018 by Teachoo
Misc 16 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): cos x 1+ sin x Let f (x) = cos x 1 + sin x Let u = cos x & v = 1 + sin x So, f(x) = f (x) = Using quotient rule f (x) = 2 Finding u & v u = cos x u = sin x & v = 1 + sin x v = 0 + cos x = cos x Now, f (x) = = 2 = ( sin ) (1 + sin ) cos ( cos ) (1 + sin x ) 2 = sin (1 + sin ) cos2 (1 + sin x ) 2 = sin sin2 cos2 (1 + sin x ) 2 = sin ( + ) (1 + sin x ) 2 = sin (1 + sin x ) 2 = (sin + 1) (1 + sin x ) 2 = (1 + sin ) (1 + sin x ) 2 = 1 1 + sin Hence f (x) = +