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Derivatives of Trigonometric Functions and Parametric Equations Worksheet

Derivatives of Trigonometric Functions and Parametric Equations Worksheet
  • Page 1
 1.  
What is the derivative of the function y = cosh- 1 (x-9b-9)?
a.
12(x-9) (x+b-18)
b.
b-9x-b
c.
12(x-b) (x-9)
d.
1(x-b) (b-9)


Answer: (c)


Correct answer : (3)
 2.  
Find the derivative of (x) = esinh- 1 (tan 8x).
a.
8sec 8x esinh- 1 (tan 8x)
b.
cos 8x esinh- 1 (tan 8x)
c.
tan 8x esinh- 1 (tan 8x)
d.
esinh- 1 (tan 8x)


Answer: (a)


Correct answer : (1)
 3.  
Find dydx for the parametric curve x = 8t, y = t - 23.
a.
- 1 8 t2
b.
- 1t2
c.
t2
d.
1t2


Answer: (a)


Correct answer : (1)
 4.  
Find dydx for the parametric curve x = 9e5t, y = te5t.
a.
e5t(1+5t)
b.
1 + 5t
c.
1+5t45
d.
15e5t


Answer: (c)


Correct answer : (3)
 5.  
Find the slope of the parametric curve x = 5cos t, y = 5sin t.
a.
cot t
b.
- tan t
c.
- cot t
d.
tan t


Answer: (c)


Correct answer : (3)
 6.  
Find dydx for the parametric curve x = 2t2 - 3, y = t + 5.
a.
4t
b.
14t
c.
14
d.
1t


Answer: (b)


Correct answer : (2)
 7.  
Find dydx for the parametric curve x = 6t, y = 10t2.
a.
t
b.
3 10(1t)
c.
10 3t
d.
1


Answer: (c)


Correct answer : (3)
 8.  
What is the derivative of y = sinh 8tt+8?
a.
8cosh 8tt+8-sinh 8t(t+8)2
b.
cosh 8tt+8+sinh 8t(t+8)2
c.
cosh t - sinh t(t+1)2
d.
cosh 8t


Answer: (a)


Correct answer : (1)
 9.  
Which of the following is the derivative of (x) = ecosh2 2x?
a.
4ecosh2 2x (cosh 2x)
b.
- ecosh2 2x (sinh 4x)
c.
2ecosh2 2x (sinh 4x)
d.
ecosh2 4x


Answer: (c)


Correct answer : (3)
 10.  
Which of the following is the derivative of (x) = 6tanh 5x + sech 5x?
a.
sech 5x (6tanh 5x + sech 5x)
b.
sech 5x (6tanh 5x - sech 5x)
c.
5sech x (6sech 5x - tanh 5x)
d.
sech 5x (tanh 5x - 6sech 5x)


Answer: (c)


Correct answer : (3)

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