7.5.1 Differentiating implicit and simple functions Quiz: Pearson Edexcel Maths, Unit 7

The 20 questions

1. What represents the derivative of y with respect to x in implicit differentiation?

   • dx/dy
   • d/dx
   • dy^2/dx
   • dy/dx

2. Which rule must be applied when differentiating a product of x and y implicitly?

   • Chain rule
   • Quotient rule
   • Power rule
   • Product rule

3. What is the implicit derivative of y^2 with respect to x?

   • 2y
   • 2y(dy/dx)
   • 2(dy/dx)
   • y^2(dy/dx)

4. When differentiating sin(y) with respect to x implicitly, what term is produced?

   • cos(y)
   • cos(y)(dy/dx)
   • -sin(y)(dy/dx)
   • sin(y)(dy/dx)

5. What is the implicit derivative of e^y with respect to x?

   • e^y
   • x(e^y)
   • e^y(dy/dx)
   • (dy/dx) / e^y

6. To find dy/dx implicitly, after differentiating an equation, what is the next main algebraic step?

   • Integrate both sides
   • Expand brackets
   • Collect dy/dx terms
   • Square both sides

7. What is the derivative of ln(y) with respect to x implicitly?

   • ln(y)(dy/dx)
   • (1/y)(dy/dx)
   • y(dy/dx)
   • 1/y

8. Which geometric feature is found by substituting coordinates into an implicit dy/dx expression?

   • Area under curve
   • Gradient of tangent
   • Inflection point
   • Second derivative

9. Find dy/dx implicitly for the circle equation x^2 + y^2 = 25.

   • x/y
   • 2x/2y
   • -x/y
   • -y/x

10. What is the value of dy/dx for x^2 + y^2 = 25 at the point (3, 4)?

    • 3/4
    • -3/4
    • -4/3
    • 4/3

11. Find dy/dx for the curve defined by xy = 6.

    • y/x
    • -y/x
    • -6/y
    • 6/x^2

12. What is the gradient of the curve xy = 6 at the point (2, 3)?

    • 3/2
    • 2/3
    • -2/3
    • -3/2

13. Differentiate x^3 + y^3 = 9 implicitly to find dy/dx.

    • -x^2 / y^2
    • -3x^2 / 3y
    • x^2 / y^2
    • -y^2 / x^2

14. Find dy/dx for the relation y^2 = x using implicit differentiation.

    • 1/2
    • 2y
    • 1/(2y)
    • 2x

15. What is the gradient of the curve y^2 = x at the point (4, 2)?

    • 1/4
    • 4
    • 2
    • 1/2

16. At what type of points on an implicitly defined curve is dy/dx equal to zero?

    • Points of inflection
    • Stationary points
    • Vertical tangents
    • Y-intercepts

17. At what type of points on an implicitly defined curve is dy/dx undefined?

    • Stationary points
    • Origin points
    • Asymptotes
    • Vertical tangents

18. Find the x-coordinate of the vertical tangent on the circle x^2 + y^2 = 25.

    • 3
    • 5
    • 0
    • 25

19. What is the value of dy/dx for the implicit equation e^(xy) = 2?

    • 1/(xy)
    • -x/y
    • y/x
    • -y/x

20. What is the gradient of the curve defined by x^2 + 3xy + y^2 = 11 at (1, 2)?

    • 8/7
    • -8/7
    • 7/8
    • -7/8

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