Pre-Calc Homework Solutions 93

Pre-Calc Homework Solutions 93 - Section 3.6 6. 7. cos x 3...

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Unformatted text preview: Section 3.6 6. 7. cos x 3 cos2 x 2 2 g(cos x) g( f (x)) g(h(cos x)) g(h( f (x))) dy dx d (x dx 2 3 3d 93 9. x) x) 2(x 1 1 2 x x) g(3 cos2 x) dx (x x) 8. 3 cos x 6 h( cos x 9. cos 27x 4 2 3(cos x 2) 3( cos x 2)2 2) h(g(cos x)) h(g( f (x))) f (3(3x 2)2) 2 2(x dy dx d (csc x dx f (27x 4) f (h(3x 2)) f ( 3x 2 f (h(h(x))) 2) 10. cot x) cot x) 1 2d cos 3x 10. cos 2 3x f (g(3x 2)) f (g(h(x))) 2 (csc x 1 dx (csc x cot x) csc2 x) Section 3.6 Exercises 1. dy dx d sin (3x dx 1) [cos (3x 3 cos (3x [cos (7 1)] (3x 1) d 5x)] (7 dx d dx (csc x cot x)2 ( cot x csc x 1) [cos (3x 2. dy dx 1)](3) 5x) (csc x)(cot x csc x) (csc x cot x)2 csc x csc x cot x d sin (7 dx 11. 5x) dy dx d (sin 5 x dx cos3 x) x) (sin x) d dx ( 5 sin 5 sin 6 6 (3 cos2 x) (cos x) [cos (7 3. dy dx 5x)]( 5) 3x) 3) x 3) 5 cos (7 5x) d dx d dx x cos x 5)4] 5)4 d dx 3 cos2 x sin x d cos ( dx [ sin ( 3x)] ( 3 sin ( 3x) [sec2 (2x 3x 2) (2 3x) 12. [ sin ( 3x)]( 4. dy dx d tan (2x dx dy dx x 3)] (2x 3x 2) sec2 (2x d (2x 1) dx 2 x d dx d 3 [x (2x dx d (x 3) (2x dx (2x 5)4 (x 3) 5) 3x 2(2x 5)4 5)] (2x 5)4 5)4(3x 2) d dx x 3) x 3) (x 3)(4)(2x (x 3)(4)(2x 8x 3(2x x 2(2x x (2x 13. dy dx 2 5)3 (2x 5)3(2) 5)3 [sec2 (2x 5. dy dx x 3)](2 2 2 d 5 cot 5 csc2 x x dx 10 2 2 2 5 csc ( 2x ) csc2 x x2 d sin x dx 1 cos x sin x 2 1 cos x (1 2 3x 2(2x 3(2x 15) 5)3[8x 5) (14x 3 6. dy dx 2 1 sin x d sin x cos x dx 1 cos x d sin x dx cos x) sin x (1 cos x) 2 d dx cos x) (1 (1 cos x (1 1 (1 1 2 2 2 1 1 1 sin x cos x sin x cos x sin x cos x cos x)(cos x) (sin x)( sin x) (1 cos x)2 cos x sin x cos x)2 dy dx 2 2 d (sin3 x tan 4x) dx d d (sin3 x) (tan 4x) (tan 4x) (sin3 x) dx dx d d (sin3 x)(sec2 4x) (4x) (tan 4x)(3 sin2 x) (sin x) dx dx (sin3 x)(sec2 4x)(4) 4 sin3 x sec2 4x d (4 dx (tan 4x)(3 sin2 x)(cos x) 3 sin2 x cos x tan 4x cos x cos x)2 1 cos x sin x 2 1 cos x 2 sin x (1 cos x)2 14. sec x 1 tan x) d (sec x tan x dx 4 tan x) sec2 x) 2 sec x 2 7. dy dx d cos (sin x) dx [ sin (sin x)] d (sin x) dx sec x tan x sec x tan x sec x (sec x tan x 2 sec x 2 sec x sin (sin x) cos x dy dx d sec (tan x) dx d dx tan x sec x tan x 8. sec (tan x) tan (tan x) (tan x) sec (tan x) tan (tan x) sec2 x ...
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