Title: Implicit Differentiation PostVideo Questions
Course: Calculus I

Q: Suppose x and y represent the measures of covarying quantities and that the covariation of x and y is constrained by the equation (x)^(2)+ 5(y)^(2)= 9. At what rate does y change with respect to x when x = 2 and y = 1?
- - 2 (Incorrect)
- - 1 (Incorrect)
- -(1)/(2) (Incorrect)
- -(2)/(5) (Incorrect)
- -(4)/(25) (Correct)
- 0 (Incorrect)
- (1)/(2) (Incorrect)
- 1 (Incorrect)
- 2 (Incorrect)
- 4 (Incorrect)
- 5 (Incorrect)
A: -(4)/(25)

Q: Suppose x and y are related by the equation cos(y)= x y. Further suppose that x changes by a very small amount, represented by d x. Write an expression for the corresponding change d y in y.
- (- y)/(sin(y)+ x)d x (Correct)
- - sin(y)d x (Incorrect)
- (y)/(- sin(y)- x)d x (Incorrect)
- (cos(y))/(x)d x (Incorrect)
- (- y)/(sin(y)+ x)d x (Incorrect)
- (- sin(y))/(x)d x (Incorrect)
A: (- y)/(sin(y)+ x)d x

Q: Determine the slope of the line tangent to the curve (x)^(2)+(y)^(2)= 25 at the point (4,3).
- (- 4)/(3) (Correct)
- (- 4)/(5) (Incorrect)
- (- 3)/(4) (Incorrect)
- 0 (Incorrect)
- (3)/(4) (Incorrect)
- (4)/(5) (Incorrect)
- 1 (Incorrect)
- (4)/(3) (Incorrect)
A: (- 4)/(3)