Product and quotient rules

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   f = 2, f′ = 3, g = 4, g′ = -1, k = 5, k′ = 2. Ari differentiates p(x) = f(x)g(x)k(x) with the values shown. What is p′(2)?

   66
2. 2.

   f = 3, f′ = -1, g = 2, g′ = 2, k = 4, k′ = 1. Esme differentiates p(x) = f(x)g(x)k(x) with the values shown. What is p′(2)?

   22
3. 3.

   f = 5, f′ = 2, g = -1, g′ = 3, k = 2, k′ = -2. Jun differentiates p(x) = f(x)g(x)k(x) with the values shown. What is p′(2)?

   36
4. 4.

   Dye in a jar has concentration C(t) = 5t/(t² + 4) grams per liter after t minutes (example data). Kira finds C′(1). What is it, in grams per liter per minute?

   3/5
5. 5.

   Dye in a jar has concentration C(t) = 6t/(t² + 16) grams per liter after t minutes (example data). Milo finds C′(2). What is it, in grams per liter per minute?

   9/50
6. 6.

   Dye in a jar has concentration C(t) = 8t/(t² + 1) grams per liter after t minutes (example data). Noah finds C′(3). What is it, in grams per liter per minute?

   -16/25
7. 7.

   Pia uses the quotient rule on h(x) = (x² + 1)/(x − 3) and simplifies the top. Which is h′(x)?

   • h′(x) = (x² − 6x − 1)/(x − 3)
   • h′(x) = 2x
   • h′(x) = (−x² + 6x + 1)/(x − 3)²
   • h′(x) = (x² − 6x − 1)/(x − 3)²
8. 8.

   Ren uses the quotient rule on h(x) = (x² − 2)/(x + 1) and simplifies the top. Which is h′(x)?

   • h′(x) = (−x² − 2x − 2)/(x + 1)²
   • h′(x) = (x² + 2x + 2)/(x + 1)²
   • h′(x) = (x² + 2x + 2)/(x + 1)
   • h′(x) = 2x
9. 9.

   Tala uses the quotient rule on h(x) = (3x + 2)/(x² + 1) and simplifies the top. Which is h′(x)?

   • h′(x) = 3/(2x)
   • h′(x) = (−3x² − 4x + 3)/(x² + 1)
   • h′(x) = (−3x² − 4x + 3)/(x² + 1)²
   • h′(x) = (3x² + 4x − 3)/(x² + 1)²
10. 10.

    Zee uses the quotient rule on h(x) = x³/(x + 2) and simplifies the top. Which is h′(x)?

    • h′(x) = 3x²
    • h′(x) = (2x³ + 6x²)/(x + 2)
    • h′(x) = (−2x³ − 6x²)/(x + 2)²
    • h′(x) = (2x³ + 6x²)/(x + 2)²