Derivatives of exponential and log functions

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari differentiates f(x) = 6 ln x. What is f′(3)?

   2
2. 2.

   Bo differentiates f(x) = 10 ln x. What is f′(4)?

   5/2
3. 3.

   Esme differentiates f(x) = 8 ln x. What is f′(2)?

   4
4. 4.

   Kira differentiates f(x) = 3ˣ. Which is f′(x)?

   • f′(x) = 3ˣ/ln 3
   • f′(x) = 3ˣ
   • f′(x) = 3ˣ ln 3
   • f′(x) = x · 3ˣ⁻¹
5. 5.

   Luz differentiates f(x) = 7 · 10ˣ. Which is f′(x)?

   • f′(x) = 7x · 10ˣ⁻¹
   • f′(x) = 7 · 10ˣ
   • f′(x) = 7 · 10ˣ/ln 10
   • f′(x) = 7 · 10ˣ ln 10
6. 6.

   Milo differentiates f(x) = log₂ x. Which is f′(x)?

   • f′(x) = 1/(2x)
   • f′(x) = 1/(x ln 2)
   • f′(x) = 1/x
   • f′(x) = (ln 2)/x
7. 7.

   Noah differentiates f(x) = 4 log₅ x. Which is f′(x)?

   • f′(x) = 4/(x ln 5)
   • f′(x) = (4 ln 5)/x
   • f′(x) = 4/x
   • f′(x) = 4/(5x)
8. 8.

   Pia differentiates f(x) = 3e^(2x) + 5x. What is f′(0)?

   11
9. 9.

   Ren differentiates f(x) = 4e^(-3x) + 7x. What is f′(0)?

   -5
10. 10.

    Zee differentiates f(x) = 5e^(-2x) + 3x. What is f′(0)?

    -7