AP Calculus AB: Chapter 6 Test
This set presents more challenging implicit differentiation exercises involving combinations of polynomial, exponential, and trigonometric expressions. It also addresses the consistency between explicit and implicit differentiation and analyzes conditions for horizontal tangent lines on implicitly defined curves.
Given 5x^ 2 + 2y ^3 = 10, find dy / dx by implicit differentiation
−5/3 x/y^2
Key Terms
Given 5x^ 2 + 2y ^3 = 10, find dy / dx by implicit differentiation
−5/3 x/y^2
Given xy = y^ 3, find dy / dx by implicit differentiation.
y/3y^2−x
Given x cos y + y cos x = 1 find dy / dx by implicit differentiation.
−cosy+ysinx/−xsiny+cosx
Given √x^3+√y^3=1, find dy/dx by implicit differentiation.
−(x/y)^1/2
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
Find all points on xy = e^xy where the tangent line is horizontal.
none of the above
Related Flashcard Decks
Study Tips
- Press F to enter focus mode for distraction-free studying
- Review cards regularly to improve retention
- Try to recall the answer before flipping the card
- Share this deck with friends to study together
| Term | Definition |
|---|---|
Given 5x^ 2 + 2y ^3 = 10, find dy / dx by implicit differentiation | −5/3 x/y^2 |
Given xy = y^ 3, find dy / dx by implicit differentiation. | y/3y^2−x |
Given x cos y + y cos x = 1 find dy / dx by implicit differentiation. | −cosy+ysinx/−xsiny+cosx |
Given √x^3+√y^3=1, find dy/dx by implicit differentiation. | −(x/y)^1/2 |
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 |
Find all points on xy = e^xy where the tangent line is horizontal. | none of the above |
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) |
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 |
What is the inverse of f(x)=3√x−1/2? | f-1(x)=8x^3+1 |
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 |
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 |
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 |
What does arctan 0 equal? | 0 |
What does arcsec 2 equal? | π / 3 |
Solve the equation arcsin x = π / 3 for x. | x=√3/2 |
Evaluate y=arcsin(cos(−π/3)). | π / 6 |
Find the derivative d/dx[(arccosx)^2]. | −2arccosx/√1−x^2 |
What does the derivative d/dx[arccot(√x)]equal? | −1/2√x(1+x) |
What is arccosh (1) equal to? | 0 |
Find d/dx[cosh(e^x)] | e^x sinh (e^x) |