12th grade Derivatives of exponential and log functions worksheet

Derivatives of exponential and log functions

Grade 12 Math Worksheet

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

1. 1.

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

   Jun uses the chain rule on f(x) = ln(x² + 8). What is f′(4)?
3. 3.

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

   • h′(x) = 2xeˣ
   • h′(x) = 2xeˣ − x²eˣ
   • h′(x) = 2xeˣ + x²eˣ
   • h′(x) = x²eˣ
4. 4.

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

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

   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 sin x
   • h′(x) = eˣ cos x
   • h′(x) = eˣ sin x + eˣ cos x
6. 6.

   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) = x²
   • h′(x) = 3x² ln x + x²
7. 7.

   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?
8. 8.

   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?
9. 9.

   Cocoa is D(t) = 60e^(−0.1t) °C above room temperature at t minutes (example data). Tala wants the rate at t = 5. In °C per minute, to the nearest hundredth, what is it?
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?