Chapter 6 Test Flashcards Preview

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Flashcards in Chapter 6 Test Deck (20):
1

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

−5/3 x/y^2

2

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

y/3y^2−x

3

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

−cosy+ysinx/−xsiny+cosx

4

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

−(x/y)^1/2

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.

true

6

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

none of the above

7

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

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

8

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

f(x)=x/x-1

9

What is the inverse of f(x)=3√x−1/2?

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

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?

1

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?

−1/2

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?

12

13

What does arctan 0 equal?

0

14

What does arcsec 2 equal?

π / 3

15

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

x=√3/2

16

Evaluate y=arcsin(cos(−π/3)).

π / 6

17

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

−2arccosx/√1−x^2

18

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

−1/2√x(1+x)

19

What is arccosh (1) equal to?

0

20

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

e^x sinh (e^x)

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