The chain rule

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari uses the chain rule on h(x) = √(3x + 1). What is h′(5)?

   3/8
2. 2.

   Bo uses the chain rule on h(x) = √(2x + 5). What is h′(2)?

   1/3
3. 3.

   Esme uses the chain rule on h(x) = √(5x − 1). What is h′(2)?

   5/6
4. 4.

   Jun uses the chain rule on h(x) = √(4x + 9). What is h′(4)?

   2/5
5. 5.

   Luz writes h(x) = 8/(3x + 1)² as 8(3x + 1)⁻² and uses the chain rule. What is h′(1)?

   -3/4
6. 6.

   Milo writes h(x) = 5/(2x + 1)³ as 5(2x + 1)⁻³ and uses the chain rule. What is h′(-1)?

   -30
7. 7.

   Noah writes h(x) = 9/(-2x + 5)² as 9(-2x + 5)⁻² and uses the chain rule. What is h′(1)?

   4/3
8. 8.

   f(x) = x³ − 5x and g(x) = x² + 2. Ren differentiates h(x) = f(g(x)). What is h′(1)?

   44
9. 9.

   f(x) = x³ + 4x and g(x) = x² − 3. Tala differentiates h(x) = f(g(x)). What is h′(-1)?

   -32
10. 10.

    f(x) = x³ + 3x and g(x) = x² − 4. Zee differentiates h(x) = f(g(x)). What is h′(3)?

    468