Find the derivative: choose the rule

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari is about to differentiate h(x) = x³ sin x. Which rule does the outside shape call for first?

   • the power rule alone, on x³
   • the quotient rule, for x³ over sin x
   • the chain rule, for x³ inside sin
   • the product rule, for x³ times sin x
2. 2.

   Esme is about to differentiate h(x) = eˣ/(x² + 1). Which rule does the outside shape call for first?

   • the product rule, for eˣ times x² + 1
   • the chain rule, for x² + 1 inside eˣ
   • the quotient rule, for eˣ over x² + 1
   • the power rule alone, on x²
3. 3.

   Jun is about to differentiate h(x) = √x · ln x. Which rule does the outside shape call for first?

   • the power rule alone, on √x
   • the product rule, for √x times ln x
   • the quotient rule, for √x over ln x
   • the chain rule, for ln x inside √
4. 4.

   Kira differentiates f(x) = 3x⁴ + 5 ln x term by term. What is f′(1)?

   17
5. 5.

   Milo differentiates f(x) = 4x³ + 7 ln x term by term. What is f′(1)?

   19
6. 6.

   Noah differentiates f(x) = 5x² − 6 ln x term by term. What is f′(1)?

   4
7. 7.

   Pia uses the quotient rule on f(x) = (2x + 1)/(x + 3). What is f′(1)?

   5/16
8. 8.

   Ren uses the quotient rule on f(x) = (3x − 2)/(x + 1). What is f′(2)?

   5/9
9. 9.

   Tala uses the quotient rule on f(x) = (4x + 5)/(x + 2). What is f′(0)?

   3/4
10. 10.

    Zee uses the quotient rule on f(x) = (5x + 3)/(x − 1). What is f′(3)?

    -2