Chapter 5 Test

Question 1

If sin x = 3/5, what is tan x ?

Answer 1

3/4

Question 2

Find dy/dx of y=(3x^2−2)sin2x

Answer 2

6xsin^2x+2(3x^2−2)sinxcosx

Question 3

Compute the derivative of the function f(x)=x^2−1/sinx?

Answer 3

2xcscx−(x^2−1)cotxcscx

Question 4

Compute the derivative of the function f (x) = sec x.

Answer 4

tan x sec x

Question 5

What is the derivative of the function f(x)=sin^2x+tan(x^2+1)?

Answer 5

2sinxcosx+2xsec^2(x^2+1)

Question 6

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

Answer 6

−2cosx/(sinx−1)^2

Question 7

Find the derivative of f(x)=e^x^2.

Answer 7

2xe^x^2

Question 8

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

Answer 8

e^x+e^−x/2

Question 9

What is the derivative of y=e^x−e^−x/e^x+e^−x?

Answer 9

4/(e^x+e^−x)^2

Question 10

What is the derivative of the function

f(x) =e^x^2−1/1+sinx?

Answer 10

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

Question 11

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

Answer 11

e^sinx*cosx

Question 12

What is the derivative of the function f(x) =x^3+2e^2x?

Answer 12

3x^2+4e^2x

Question 13

What is the derivative of the function

f(x) =sinx(1+e−x)/1+x?

Answer 13

(1+x)[(1+e^−x)cosx+(−e^−x)sinx]−(1+e^−x)sinx/(1+x)^2

Question 14

What is the derivative of f(x)=ln1/x?

Answer 14

−1/x

Question 15

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

Answer 15

2x ln x + x

Question 16

What is the derivative of the function f(x)=lnx−1/lnx+1

Answer 16

2/x(lnx+1)^2

Question 17

What is the derivative of the function

f (x) = log _x  2?

Answer 17

−ln2/x(lnx)^2

Question 18

What is the derivative of the function

f(x)=ln(x+√x^2−1)?

Answer 18

1/x+√x^2−1 * (1+x/√x^2−1)

Question 19

What is the derivative of the function

f(x)=ln√x+1/x−1?

Answer 19

−1/(x+1)(x−1)

Question 20

What is the derivative of the function

f(x)=lnx/lnx−1?

Answer 20

−1/x(lnx−1)^2