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Flashcards in Chapter 6 Test Deck (20)
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1
Q

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

A

−5/3 x/y^2

2
Q

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

A

y/3y^2−x

3
Q

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

A

−cosy+ysinx/−xsiny+cosx

4
Q

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

A

−(x/y)^1/2

5
Q

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.

A

true

6
Q

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

A

none of the above

7
Q

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

A

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

8
Q

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

A

f(x)=x/x-1

9
Q

What is the inverse of f(x)=3√x−1/2?

A

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

10
Q

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?

A

1

11
Q

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?

A

−1/2

12
Q

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?

A

12

13
Q

What does arctan 0 equal?

A

0

14
Q

What does arcsec 2 equal?

A

π / 3

15
Q

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

A

x=√3/2

16
Q

Evaluate y=arcsin(cos(−π/3)).

A

π / 6

17
Q

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

A

−2arccosx/√1−x^2

18
Q

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

A

−1/2√x(1+x)

19
Q

What is arccosh (1) equal to?

A

0

20
Q

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

A

e^x sinh (e^x)

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