Answers – Trig in Calculus

1)    y’ = 5sec2 x
2)    y’ = -5csc x cot x
3)    y’ = -5csc x cot x tan x + 5csc x sec2 x = 5csc x (sec2 x – 1)
4)    y’ = (-5csc x cot x tan x – 5 csc x sec2 x)/(tan2 x) = -5 csc x (tan2 x)/(tan2 x) = -5 csc x
5)    y’ = - sin x/cos x = - tan x
6)    y’ = cos x ln (sin x) + sin x cos x/sin x = cos x [ln (sin x) + 1]
7)    y’ = (cos x tan x + sin x sec2 x)(esin x tan x)
8)    y’ = 2x(sec x2)(tan x2)sec2 (sec x2)
9)    y’ = 3tan2 x sec2 x
10)  y’ = (15x2)(cos 5x3)(5sin4 5x3) = 75x2cos 5x3sin4 5x3
11)  y’ = 7(5ln x + 5)cos (5xln x)
12)  y’ = 14x sin (5xln x) + 7x2(5ln x + 5)cos (5xln x)
13)  y’ = 35(ln e2x)4(2e2x/e2x) [tan2 (xcos 4x)] + 7(ln e2x)5[2tan (xcos 4x)][sec2 (xcos 4x)](cos 4x - 4xsin 4x)
       I hope you don’t see such a problem on a test!
       (Thanks Arye for correction)
14)  y’ = [(sin x2)/x – 2xsin x2 ln x]/sin2 x2
15)  y’ = -2sin-3 x
16)  y’ = ex(3/2)sin1/2 ex

 

Copyright 2001 Bruce
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