Chapter 6 Test

Question 1

Given 5x^ 2 + 2y ^3 = 10, find dy / dx by implicit differentiation

Answer 1

−5/3 x/y^2

Question 2

Given xy = y^ 3, find dy / dx by implicit differentiation.

Answer 2

y/3y^2−x

Question 3

Given x cos y + y cos x = 1 find dy / dx by implicit differentiation.

Answer 3

−cosy+ysinx/−xsiny+cosx

Question 4

Given √x^3+√y^3=1, find dy/dx by implicit differentiation.

Answer 4

−(x/y)^1/2

Question 5

Evaluate the following as true or false. If x=ye^y then the explicit differentiation to find dx/dy, and the implicit differentiation to find dy/dx yield consistent results.

Answer 5

true

Question 6

Find all points on xy = e^xy where the tangent line is horizontal.

Answer 6

none of the above

Question 7

Find all the points on the curve x ^2 − xy + y^ 2 = 4 where the tangent line has a slope equal to −1.

Answer 7

(2, 2) and (-2, -2)

Question 8

Which of the following functions is its own inverse? That is, for which of the following functions is f −1 (x) = f (x)?

Answer 8

f(x)=x/x-1

Question 9

What is the inverse of f(x)=3√x−1/2?

Answer 9

f-1(x)=8x^3+1

Question 10

What is the value of d/dx[f−1(x)] when x=π, given that f(x)=2x+sinxcosx and f−1(π)=π/2?

Answer 10

1

Question 11

What is the value of d/dx[f−1(x)] when x=2, given that f(x)=2−x^2/1+x and f−1(2)=0?

Answer 11

−1/2

Question 12

What is the value of d/dx[f−1(x)] when x=2, given that f(x)=−3√1−x and f−1(2)=9?

Answer 12

12

Question 13

What does arctan 0 equal?

Answer 13

0

Question 14

What does arcsec 2 equal?

Answer 14

π / 3

Question 15

Solve the equation arcsin x = π / 3 for x.

Answer 15

x=√3/2

Question 16

Evaluate y=arcsin(cos(−π/3)).

Answer 16

π / 6

Question 17

Find the derivative d/dx[(arccosx)^2].

Answer 17

−2arccosx/√1−x^2

Question 18

What does the derivative d/dx[arccot(√x)]equal?

Answer 18

−1/2√x(1+x)

Question 19

What is arccosh (1) equal to?

Answer 19

0

Question 20

Find d/dx[cosh(e^x)]

Answer 20

e^x sinh (e^x)