Power, sum and difference rules

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari uses the power rule on f(x) = 12x^(2/3). What is f′(27)?

   8/3
2. 2.

   Esme uses the power rule on f(x) = 4x^(3/2). What is f′(9)?

   18
3. 3.

   Jun uses the power rule on f(x) = 6x^(1/3). What is f′(8)?

   1/2
4. 4.

   Kira splits f(x) = (3x³ + 8)/x into 3x² + 8x⁻¹ before using the power rule. What is f′(2)?

   10
5. 5.

   Luz splits f(x) = (2x³ + 18)/x into 2x² + 18x⁻¹ before using the power rule. What is f′(3)?

   10
6. 6.

   Milo splits f(x) = (5x³ − 16)/x into 5x² − 16x⁻¹ before using the power rule. What is f′(2)?

   24
7. 7.

   Pia writes f(x) = 4√x − 6/x + x³ with powers: x^(1/2), x⁻¹ and x³. Which is f′(x)?

   • f′(x) = 2/√x + 6/x² + 3x²
   • f′(x) = 2/√x − 6/x² + 3x²
   • f′(x) = 2√x + 6/x² + 3x²
   • f′(x) = 2/√x + 6 + 3x²
8. 8.

   Ren writes f(x) = 6√x + 8/x − 2x² with powers: x^(1/2), x⁻¹ and x². Which is f′(x)?

   • f′(x) = 3√x − 8/x² − 4x
   • f′(x) = 3/√x − 8/x² − 4x
   • f′(x) = 3/√x + 8/x² − 4x
   • f′(x) = 3/√x − 8 − 4x
9. 9.

   Tala writes f(x) = 10√x − 3/x + 5x with powers: x^(1/2), x⁻¹ and x¹. Which is f′(x)?

   • f′(x) = 5/√x − 3/x² + 5
   • f′(x) = 5/√x + 3/x² + 5
   • f′(x) = 5√x + 3/x² + 5
   • f′(x) = 5/√x + 3 + 5
10. 10.

    Zee writes f(x) = 2√x + 5/x + x⁴ with powers: x^(1/2), x⁻¹ and x⁴. Which is f′(x)?

    • f′(x) = 1/√x + 5/x² + 4x³
    • f′(x) = 1/√x − 5 + 4x³
    • f′(x) = 1/√x − 5/x² + 4x³
    • f′(x) = √x − 5/x² + 4x³