12th grade Derivatives of trig functions worksheet

Derivatives of trig functions

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)?
9. 9.

   Ren uses the chain rule on f(x) = sin(2x). What is f′(π/3)?
10. 10.

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