Find the derivative: choose the rule

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   At x = 2, 7, 6, 3, 4; at x = 3, 5, -2, 8, 0. h(x) = x · f(g(x)). Ari uses the table shown and picks the rules. What is h′(2)?

   -11
2. 2.

   At x = 1, 2, 5, 4, 3; at x = 4, 8, 2, 0, 7. h(x) = x · f(g(x)). Bo uses the table shown and picks the rules. What is h′(1)?

   14
3. 3.

   At x = -1, 3, 0, 2, 5; at x = 2, -4, 3, 6, 1. h(x) = x · f(g(x)). Esme uses the table shown and picks the rules. What is h′(-1)?

   -19
4. 4.

   At x = 3, 1, 4, -2, -1; at x = -2, 5, 6, 3, 2. h(x) = x · f(g(x)). Jun uses the table shown and picks the rules. What is h′(3)?

   -13
5. 5.

   Kira picks the rules for h(x) = sin(2x)/x² and simplifies. Which is h′(x)?

   • h′(x) = (2x cos(2x) + 2 sin(2x))/x³
   • h′(x) = (2x cos(2x) − 2 sin(2x))/x
   • h′(x) = (x cos(2x) − 2 sin(2x))/x³
   • h′(x) = (2x cos(2x) − 2 sin(2x))/x³
6. 6.

   Luz picks the rules for h(x) = e^(3x)/(x + 1) and simplifies. Which is h′(x)?

   • h′(x) = e^(3x)(3x + 2)/(x + 1)
   • h′(x) = e^(3x)(3x + 2)/(x + 1)²
   • h′(x) = xe^(3x)/(x + 1)²
   • h′(x) = −e^(3x)(3x + 2)/(x + 1)²
7. 7.

   Milo picks the rules for h(x) = x² ln(3x) and simplifies. Which is h′(x)?

   • h′(x) = 2x ln(3x) + x
   • h′(x) = 2x ln(3x) + x/3
   • h′(x) = 2x ln(3x) − x
   • h′(x) = x
8. 8.

   Noah picks the rules for h(x) = xe^(−x²) and simplifies. Which is h′(x)?

   • h′(x) = e^(−x²) − 2x²e^(−x²)
   • h′(x) = e^(−x²) + 2x²e^(−x²)
   • h′(x) = −2x²e^(−x²)
   • h′(x) = e^(−x²) + xe^(−x²)
9. 9.

   Pia picks the chain rule for f(x) = arctan(2x). What is f′(1)?

   0.4
10. 10.

    Tala picks the chain rule for f(x) = arctan(4x). What is f′(0.5)?

    0.8