Derivatives of trig functions

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari uses the product rule on h(x) = x² sin x. Which is h′(x)?

   • h′(x) = 2x sin x + x² cos x
   • h′(x) = 2x sin x − x² cos x
   • h′(x) = 2x cos x
   • h′(x) = x² cos x
2. 2.

   Bo uses the product rule on h(x) = x cos x. Which is h′(x)?

   • h′(x) = cos x + x sin x
   • h′(x) = −x sin x
   • h′(x) = −sin x
   • h′(x) = cos x − x sin x
3. 3.

   Esme uses the product rule on h(x) = x³ tan x. Which is h′(x)?

   • h′(x) = 3x² tan x − x³ sec² x
   • h′(x) = 3x² sec² x
   • h′(x) = 3x² tan x + x³ sec² x
   • h′(x) = x³ sec² x
4. 4.

   Jun uses the product rule on h(x) = 5x sec x. Which is h′(x)?

   • h′(x) = 5 sec x − 5x sec x tan x
   • h′(x) = 5x sec x tan x
   • h′(x) = 5 sec x tan x
   • h′(x) = 5 sec x + 5x sec x tan x
5. 5.

   Luz uses the quotient rule on h(x) = x / cos x. Which is h′(x)?

   • h′(x) = (cos x + x sin x)/cos² x
   • h′(x) = (cos x + x sin x)/cos x
   • h′(x) = −1/sin x
   • h′(x) = (−cos x − x sin x)/cos² x
6. 6.

   Milo uses the quotient rule on h(x) = x² / sin x. Which is h′(x)?

   • h′(x) = (2x sin x − x² cos x)/sin x
   • h′(x) = (2x sin x − x² cos x)/sin² x
   • h′(x) = 2x/cos x
   • h′(x) = (x² cos x − 2x sin x)/sin² x
7. 7.

   Noah uses the quotient rule on h(x) = cos x / x. Which is h′(x)?

   • h′(x) = −sin x
   • h′(x) = (−x sin x − cos x)/x²
   • h′(x) = (−x sin x − cos x)/x
   • h′(x) = (x sin x + cos x)/x²
8. 8.

   Pia uses the chain rule on f(x) = sin(3x). What is f′(π/9)?

   3/2
9. 9.

   Ren uses the chain rule on f(x) = sin(2x). What is f′(π/3)?

   -1
10. 10.

    Zee uses the chain rule on f(x) = sin(4x). What is f′(π/3)?

    -2