1.07q Techniques of differentiation Quiz: OCR Maths, Unit 7

The 20 questions

1. Which is the product rule?

   • (uv)' = u'v'
   • (uv)' = u'v + uv'
   • (uv)' = u'v - uv'
   • (uv)' = uv(u' + v')

2. Which is the quotient rule for (u/v)'?

   • (u'v - uv')/v^2
   • (u'v + uv')/v^2
   • u'/v'
   • (uv' - u'v)/v

3. What is the derivative of x e^x?

   • e^x - x e^x
   • x e^x
   • e^x + x e^x
   • e^x

4. What is the derivative of x^2 sin x?

   • 2x sin x - x^2 cos x
   • 2x sin x + x^2 cos x
   • 2x cos x + x^2 sin x
   • x^2 cos x

5. What is the derivative of x^3 ln x?

   • 3x^2 ln x + x^2
   • x^3 / x
   • 3x^2 / x
   • 3x^2 ln x - x^2

6. What is the derivative of (x + 1)/(x - 1)?

   • 2/(x - 1)^2
   • 1/(x - 1)^2
   • -2/(x - 1)^2
   • -2/(x + 1)^2

7. What is the derivative of e^x / x?

   • e^x / x^2
   • e^x (x + 1)/x^2
   • e^x / (x - 1)
   • e^x (x - 1)/x^2

8. What is the gradient of y = x e^x at x = 0?

   • e
   • 1
   • 2
   • 0

9. What is the derivative of x^2/(x + 1)?

   • 2x/(x + 1)
   • (x^2 - 2x)/(x + 1)^2
   • (x^2 + 2x)/(x + 1)^2
   • (2x + 1)/(x + 1)^2

10. What is the derivative of x^2 e^(2x)?

    • 2x(1 - x) e^(2x)
    • 2x e^(2x)
    • 2x(1 + x) e^(2x)
    • 2x^2 e^(2x)

11. If f(x) = x^2 g(x), with g(2) = 3 and g'(2) = -1, what is f'(2)?

    • 4
    • 8
    • -8
    • 12

12. What is the derivative of 3x/(x^2 + 1) at x = 1?

    • 3/2
    • 0
    • 3/4
    • -3/2

13. For f(x) = x^2/(x - 2), where is f'(x) = 0?

    • x = 4 only
    • x = -4 and x = 0
    • x = 2 only
    • x = 0 and x = 4

14. Find the gradient of y = x^2 ln x at x = e.

    • 3e
    • e
    • 2e
    • 4e

15. What is the derivative of x^n e^x?

    • e^x (x^n - n x^(n - 1))
    • e^x x^n (n + 1)
    • e^x (x^n + n x^(n - 1))
    • n x^(n - 1) e^x

16. Using the quotient rule, what is d/dx (sin x / cos x)?

    • 1/cos^2 x
    • -1/sin^2 x
    • cos x / sin x
    • sec x tan x

17. What is the derivative of sin x cos x?

    • cos^2 x - sin^2 x
    • cos^2 x + sin^2 x
    • 2 sin x cos x
    • sin^2 x - cos^2 x

18. What is the derivative of 1/x using the quotient rule?

    • 1/x
    • -1/x
    • -1/x^2
    • 1/x^2

19. What is the derivative of x e^(-x)?

    • (1 + x) e^(-x)
    • -x e^(-x)
    • (1 - x) e^(-x)
    • e^(-x)

20. What is the derivative of x ln x?

    • ln x + 1
    • ln x
    • x/ln x
    • 1/x

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