The chain rule

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari uses the chain rule on h(x) = (3x − 4)⁴. What is h′(1)?

   -12
2. 2.

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

   36
3. 3.

   At x = 1, 3, 2, 5; at x = 3, 0, 1, -4. Kira uses the table shown. If h(x) = f(g(x)), what is h′(1)?

   -8
4. 4.

   At x = 2, -1, 3, 4; at x = -1, 5, 0, 2. Luz uses the table shown. If h(x) = f(g(x)), what is h′(2)?

   6
5. 5.

   At x = 0, 4, -2, 7; at x = 4, 1, 3, 5. Milo uses the table shown. If h(x) = f(g(x)), what is h′(0)?

   -10
6. 6.

   At x = 3, 2, 4, -1; at x = 2, 6, 1, 3. Noah uses the table shown. If h(x) = f(g(x)), what is h′(3)?

   12
7. 7.

   Pia names the inside u = x² + 5 and uses the chain rule on h(x) = (x² + 5)³. Which is h′(x)?

   • h′(x) = 6x(x² + 5)³
   • h′(x) = 3(x² + 5)²
   • h′(x) = 3(2x)²
   • h′(x) = 6x(x² + 5)²
8. 8.

   Ren names the inside u = 4x − 1 and uses the chain rule on h(x) = (4x − 1)⁵. Which is h′(x)?

   • h′(x) = 5(4x − 1)⁴
   • h′(x) = 20(4x − 1)⁴
   • h′(x) = 20(4x − 1)⁵
   • h′(x) = 5 × 4⁴
9. 9.

   Tala names the inside u = x² + 9 and uses the chain rule on h(x) = √(x² + 9). Which is h′(x)?

   • h′(x) = 1/(2√(x² + 9))
   • h′(x) = x/√(x² + 9)
   • h′(x) = x√(x² + 9)
   • h′(x) = 1/(2√(2x))
10. 10.

    Zee names the inside u = x³ − 2x and uses the chain rule on h(x) = (x³ − 2x)⁴. Which is h′(x)?

    • h′(x) = 4(x³ − 2x)³(3x² − 2)
    • h′(x) = 4(3x² − 2)³
    • h′(x) = 4(x³ − 2x)⁴(3x² − 2)
    • h′(x) = 4(x³ − 2x)³