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Math 113 – Homework 6 – Solutions Due: 15 December 2005 Thursday. Find the derivatives of the given functions with respect to x and write your answers in the spaces provided. Do not simplify. Leave your answer in a format which is easy to read. 1 f (x) = xx 2 f (x) = (ln x)ln x 3 f (x) = xcos x Z 4 tan x f (x) = √ f 0 (x) = xx (ln x + 1) 1 1 1 f 0 (x) = (ln x)ln x ( ln ln x + ln x ) x ln x x f 0 (x) = xcos x (− sin x ln x + cos x 1 + t3 dt f 0 (x) = p 1 + tan3 x sec2 x − √ 1 ) x 1 + sec3 x sec x tan x sec x 5 f (x) = sec x + ln tan x 1 x f 0 (x) = sec x tan x + f 0 (x) = sin 1 sec2 x tan x 1 1 −1 + x cos x x x2 6 f (x) = x sin 7 x2 + 1 f (x) = 3 x +1 8 f (x) = (cos x)(ln x) f 0 (x) = − sin x ln x + cos x 9 f (x) = (cos x)2 ln x f 0 (x) = 2(cos x)(− sin x) ln x + (cos x)2 10 f (x) = (cos x)2 (ln x)3 2x(x3 + 1) − (x2 + 1)(3x2 ) f (x) = (x3 + 1)2 0 1 x 1 x f 0 (x) = 2(cos x)(− sin x)(ln x)3 + (cos x)2 3(ln x)2 Comments and questions to [email protected] 1 x