Find the derivative: choose the rule

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari differentiates h(x) = e^(2x) sin x, which needs two rules. Which is h′(x)?

   • h′(x) = 2e^(2x) sin x + e^(2x) cos x
   • h′(x) = 2e^(2x) sin x
   • h′(x) = 2e^(2x) sin x − e^(2x) cos x
   • h′(x) = e^(2x) sin x + e^(2x) cos x
2. 2.

   Bo differentiates h(x) = x² cos(3x), which needs two rules. Which is h′(x)?

   • h′(x) = −3x² sin(3x)
   • h′(x) = 2x cos(3x) − 3x² sin(3x)
   • h′(x) = 2x cos(3x) − x² sin(3x)
   • h′(x) = 2x cos(3x) + 3x² sin(3x)
3. 3.

   Esme differentiates h(x) = x ln(5x), which needs two rules. Which is h′(x)?

   • h′(x) = ln(5x) − 1
   • h′(x) = ln(5x) + 1
   • h′(x) = 1
   • h′(x) = ln(5x) + 1/5
4. 4.

   Jun differentiates h(x) = x³e^(−2x), which needs two rules. Which is h′(x)?

   • h′(x) = −2x³e^(−2x)
   • h′(x) = 3x²e^(−2x) + x³e^(−2x)
   • h′(x) = 3x²e^(−2x) + 2x³e^(−2x)
   • h′(x) = 3x²e^(−2x) − 2x³e^(−2x)
5. 5.

   Kira picks the chain rule for f(x) = √(x² + 9). What is f′(4)?

   4/5
6. 6.

   Milo picks the chain rule for f(x) = √(x² + 5). What is f′(2)?

   2/3
7. 7.

   Pia first splits f(x) = ln((x + 1)/(x + 3)) into ln(x + 1) − ln(x + 3). What is f′(1)?

   1/4
8. 8.

   Ren first splits f(x) = ln((x + 2)/(x − 1)) into ln(x + 2) − ln(x − 1). What is f′(3)?

   -3/10
9. 9.

   Tala first splits f(x) = ln((x + 5)/(x + 1)) into ln(x + 5) − ln(x + 1). What is f′(1)?

   -1/3
10. 10.

    Zee first splits f(x) = ln((x + 3)/(x + 7)) into ln(x + 3) − ln(x + 7). What is f′(1)?

    1/8