Product and quotient rules

Answer Key - Grade 12 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari uses the quotient rule on h(x) = (x² + 5)/(x + 1). What is h′(2)?

   1/3
2. 2.

   Bo uses the quotient rule on h(x) = (x² − 3)/(x + 2). What is h′(4)?

   35/36
3. 3.

   Jun uses the quotient rule on h(x) = (x² + 1)/(x + 3). What is h′(-1)?

   -3/2
4. 4.

   Kira uses the product rule on h(x) = (2x + 1)√x. Which is h′(x)?

   • h′(x) = 1/√x
   • h′(x) = 2√x − (2x + 1)/(2√x)
   • h′(x) = 2√x + (2x + 1)/(2√x)
   • h′(x) = 2√x
5. 5.

   Luz uses the product rule on h(x) = (x² − 3)√x. Which is h′(x)?

   • h′(x) = 2x√x + (x² − 3)/(2√x)
   • h′(x) = 2x√x
   • h′(x) = x/√x
   • h′(x) = 2x√x − (x² − 3)/(2√x)
6. 6.

   Milo uses the product rule on h(x) = (5x − 2)√x. Which is h′(x)?

   • h′(x) = 5√x − (5x − 2)/(2√x)
   • h′(x) = 5/2/√x
   • h′(x) = 5√x
   • h′(x) = 5√x + (5x − 2)/(2√x)

7. Read this first

   Values now (example data)

   Price p = $2 per cup, p′ = $0.10 per week; sales q = 150 cups a week, q′ = −4 per week.

8. 7.

   Weekly revenue is R = pq, price times weekly sales, with the values shown. Pia finds how fast R changes. What is R′, in dollars per week?

   7

9. Values now (example data)

   Price p = $3 per bag, p′ = −$0.20 per week; sales q = 80 bags a week, q′ = 6 per week.

10. 8.

    Weekly revenue is R = pq, price times weekly sales, with the values shown. Ren finds how fast R changes. What is R′, in dollars per week?

    2

11. Values now (example data)

    Length L = 12 cm, L′ = 0.5 cm per s; width W = 8 cm, W′ = −0.25 cm per s.

12. 9.

    A rectangle's area is A = LW, with the values shown. Tala finds how fast the area changes. What is A′, in cm² per second?

    1

13. Values now (example data)

    Length L = 20 cm, L′ = −0.4 cm per s; width W = 15 cm, W′ = 0.6 cm per s.

14. 10.

    A rectangle's area is A = LW, with the values shown. Zee finds how fast the area changes. What is A′, in cm² per second?

    6