Chapter 5 Practice Test

Question 1

If sin x = 1/3, what is cos x ?

Answer 1

2√2/3

Question 2

What is the derivative of f (x) = x sin x ?

Answer 2

sin x + x cos x

Question 3

Compute the derivative of the function f(x)=cot(2x−1)?

Answer 3

-2csc^2(2x-1)

Question 4

Compute the derivative of the function f(x)=tan(2x+1).

Answer 4

2sec^2(2x + 1)

Question 5

What is the derivative of the function

f(x)=sin^3x+sec^3x?

Answer 5

3sin^2xcosx+3sec^3xtanx

Question 6

What is the derivative of the function

f(x)=xsinx+1/cosx?

Answer 6

sinxcosx+x+sinx/cos^2x

Question 7

What is the derivative of f(x)=e^2x

Answer 7

2e^2x

Question 8

What is the derivative of y=xe^x+x^2 ?

Answer 8

e^x + xe^x + 2x

Question 9

What is the derivative of f(x)=e^x+e−x/2?

Answer 9

e^x−e^−x/2

Question 10

What is the derivative of the function f(x)=e^x−1/x^2+1?

Answer 10

x^2ex−2xex+ex+2x/(x^2+1)^2

Question 11

What is the derivative of the function f(x)=e^xsinx?

Answer 11

e^xcosx+e^xsinx

Question 12

What is the derivative of the function f(x) =e^x+1−1?

Answer 12

e^x+1

Question 13

What is the derivative of the function

f(x) =x sinx/e^x−1?

Answer 13

(sinx+xcosx)(e^x−1)−xe^x sinx/(e^x−1)^2

Question 14

What is the derivative of f (x) = ln 2x ?

Answer 14

1 / x

Question 15

What is the derivative of f (x) = 2^x?

Answer 15

2^x ln 2

Question 16

What is the derivative of y = x ln x − x ?

Answer 16

ln x

Question 17

What is the derivative of the function

f (x) = sin x (e^x ) − cos x (e ^2x )?

Answer 17

e^x cos x + e^x sin x + e^2x sin x − 2e^2x cos x

Question 18

What is the derivative of the function

f (x) = x^x?

Answer 18

x^x(lnx+1)

Question 19

What is the derivative of the function f(x)=√ln2x?

Answer 19

1/2x√ln2x

Question 20

What is the derivative of the function

f (x) = ln (x + ln x)?

Answer 20

1/x+lnx (1+1x)