Derivatives of exponential and log functions

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 f(x) = ln(x² + 5). What is f′(2)?

   4/9
2. 2.

   Bo uses the chain rule on f(x) = ln(x² + 7). What is f′(3)?

   3/8
3. 3.

   Esme uses the chain rule on f(x) = ln(x² − 3). What is f′(2)?

   4
4. 4.

   Jun uses the chain rule on f(x) = ln(x² + 8). What is f′(4)?

   1/3
5. 5.

   Kira uses the product rule on h(x) = x²eˣ. Which is h′(x)?

   • h′(x) = x²eˣ
   • h′(x) = 2xeˣ
   • h′(x) = 2xeˣ + x²eˣ
   • h′(x) = 2xeˣ − x²eˣ
6. 6.

   Milo uses the product rule on h(x) = eˣ sin x. Which is h′(x)?

   • h′(x) = eˣ sin x + eˣ cos x
   • h′(x) = eˣ cos x
   • h′(x) = eˣ sin x
   • h′(x) = eˣ sin x − eˣ cos x
7. 7.

   Noah uses the product rule on h(x) = x³ ln x. Which is h′(x)?

   • h′(x) = 3x
   • h′(x) = 3x² ln x − x²
   • h′(x) = 3x² ln x + x²
   • h′(x) = x²
8. 8.

   A savings account holds A(t) = 500e^(0.04t) dollars after t years (example data). Pia wants the rate at t = 10. In dollars per year, to the nearest hundredth, what is it?

   29.84
9. 9.

   A town's population is N(t) = 2000e^(0.03t) people after t years (example data). Ren wants the rate at t = 5. In people per year, to the nearest hundredth, what is it?

   69.71
10. 10.

    A tank holds V(t) = 800e^(−0.05t) liters after t minutes (example data). Zee wants the rate at t = 10. In liters per minute, to the nearest hundredth, what is it?

    -24.26