Power, sum and difference rules

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari uses the power rule on f(x) = 3x⁴. What is f′(2)?

   96
2. 2.

   Esme uses the power rule on f(x) = -2x⁴. What is f′(3)?

   -216
3. 3.

   Jun uses the power rule on f(x) = 7x³. What is f′(-2)?

   84
4. 4.

   Kira differentiates f(x) = 2x³ + 3x² + 4x + 5 term by term. Type powers like x^2. What is f′(x)?

   6x^2 + 6x + 4
5. 5.

   Milo differentiates f(x) = 5x³ + 2x² + 3x + 9 term by term. Type powers like x^2. What is f′(x)?

   15x^2 + 4x + 3
6. 6.

   Noah differentiates f(x) = 3x³ + 5x² + 2x + 6 term by term. Type powers like x^2. What is f′(x)?

   9x^2 + 10x + 2
7. 7.

   Pia rewrites f(x) = 16/x² as 16x⁻² and uses the power rule. What is f′(2)?

   -4
8. 8.

   Ren rewrites f(x) = 54/x³ as 54x⁻³ and uses the power rule. What is f′(3)?

   -2
9. 9.

   Tala rewrites f(x) = 24/x⁴ as 24x⁻⁴ and uses the power rule. What is f′(2)?

   -3
10. 10.

    Zee rewrites f(x) = 4/x² as 4x⁻² and uses the power rule. What is f′(4)?

    -1/8