Section 5.5 Extra Practice Answers
dy
⫽ 4 sec2 (4x)
1. a.
dx
dy
⫽ 42 sec2 (7x) ⫺ 3 sec2 (⫺x)
b.
dx
dy
⫽ 8x 3 tan (x 4 ) sec2 (x 4 )
c.
dx
dy
⫽ 2 sin x sec2 (2x) ⫹ cos x tan (2x)
d.
dx
5. a. 2 sec2x tan x
b. ⫺4 sec2x tan x ⫹ 4 tan2x sec2x ⫹ 2 sec4x
dy
3x sec2 (3x) ⫺ tan (3x)
⫽
2. a.
dx
3x 2
dy
⫽ 2x tan x sec 2 (x 2 ) ⫹ tan (x 2 )sec 2x
b.
dx
dy
⫽ ⫺sin x sec2 (cos x)
c.
dx
dy
⫽ (sec2x)(e tan x )
d.
dx
8. a. 6.45
b. 0
c. 1
3. a. ⫺12x ⫹ y ⫺ A3兹3 ⫺ 4␲B ⫽ 0
b. 6x ⫹ y ⫺ a1 ⫹
3␲
b ⫽0
2
6. a. ⫺2
b. 0.44
c. 4
7. minimum: (⫺0.62, ⫺0.43), maximum:
(0.62, 0.43)
9. a. 5 sec x tan x
b. sec2x (2tan x ) ln 2
c. e x sec2 (e x )
10. a. 4x sec2x ⫹ 4 tan x
b. ⫺2x sec2 (3 ⫺ x 2 )
e x tan x ⫺ e x sec2x
c.
tan2x
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4. a. cos (tan x)sec2x
b. 16x 3sec2 (4x 4 ⫹ 8)
c. 3 sin x sec2x tan2x ⫹ cos x tan3x
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Calculus and Vectors: Section 5.5 Extra Practice Answers