Flashcards in Chapter 6 Test Deck (20):
Given 5x^ 2 + 2y ^3 = 10, find dy / dx by implicit differentiation
Given xy = y^ 3, find dy / dx by implicit differentiation.
Given x cos y + y cos x = 1 find dy / dx by implicit differentiation.
Given √x^3+√y^3=1, find dy/dx by implicit differentiation.
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.
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)?
What is the inverse of f(x)=3√x−1/2?
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?
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?
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?
What does arctan 0 equal?
What does arcsec 2 equal?
π / 3
Solve the equation arcsin x = π / 3 for x.
π / 6
Find the derivative d/dx[(arccosx)^2].
What does the derivative d/dx[arccot(√x)]equal?
What is arccosh (1) equal to?