The chain rule

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari uses the product rule and the chain rule on h(x) = x(2x − 3)³. What is h′(2)?

   13
2. 2.

   Bo uses the product rule and the chain rule on h(x) = x(3x − 4)². What is h′(2)?

   28
3. 3.

   Jun uses the product rule and the chain rule on h(x) = x(5x − 9)³. What is h′(2)?

   31
4. 4.

   Kira writes h(x) = 50/√(x² + 16) as 50(x² + 16)^(−1/2) and uses the chain rule. What is h′(3)?

   -6/5
5. 5.

   Luz writes h(x) = 54/√(x² + 5) as 54(x² + 5)^(−1/2) and uses the chain rule. What is h′(2)?

   -4
6. 6.

   Milo writes h(x) = 80/√(x² + 15) as 80(x² + 15)^(−1/2) and uses the chain rule. What is h′(1)?

   -5/4
7. 7.

   Noah writes h(x) = 48/√(x² + 12) as 48(x² + 12)^(−1/2) and uses the chain rule. What is h′(2)?

   -3/2
8. 8.

   f is a function with derivative f′. Pia differentiates h(x) = f(x³) with the chain rule. Which is h′(x)?

   • h′(x) = f′(3x²)
   • h′(x) = 3x²f′(x³)
   • h′(x) = 3x²f′(x)
   • h′(x) = f′(x³)
9. 9.

   f is a function with derivative f′. Ren differentiates h(x) = f(√x) with the chain rule. Which is h′(x)?

   • h′(x) = f′(x)/(2√x)
   • h′(x) = f′(√x)/(2√x)
   • h′(x) = f′(1/(2√x))
   • h′(x) = f′(√x)
10. 10.

    f is a function with derivative f′. Zee differentiates h(x) = f(x² + 1) with the chain rule. Which is h′(x)?

    • h′(x) = 2xf′(x)
    • h′(x) = f′(2x)
    • h′(x) = f′(x² + 1)
    • h′(x) = 2xf′(x² + 1)