Second and higher derivatives

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari differentiates f(x) = (2x − 1)⁴ twice with the chain rule. What is f″(1)?

   48
2. 2.

   Bo differentiates f(x) = (3x − 2)³ twice with the chain rule. What is f″(1)?

   54
3. 3.

   Jun differentiates f(x) = (2x − 3)⁵ twice with the chain rule. What is f″(2)?

   80
4. 4.

   Kira differentiates f(x) = x sin x twice. Which is f″(x)?

   • f″(x) = −x sin x
   • f″(x) = sin x + x cos x
   • f″(x) = 2 cos x − x sin x
   • f″(x) = cos x − x sin x
5. 5.

   Milo differentiates f(x) = x cos x twice. Which is f″(x)?

   • f″(x) = −2 sin x − x cos x
   • f″(x) = cos x − x sin x
   • f″(x) = −x cos x
   • f″(x) = −sin x − x cos x
6. 6.

   Noah differentiates f(x) = x ln x twice. Which is f″(x)?

   • f″(x) = 0
   • f″(x) = −1/x
   • f″(x) = 1/x
   • f″(x) = ln x + 1
7. 7.

   f(x) = x/(x + 1) has f′(x) = 1/(x + 1)². Pia differentiates again. What is f″(2)?

   -2/27
8. 8.

   f(x) = x/(x + 3) has f′(x) = 3/(x + 3)². Ren differentiates again. What is f″(1)?

   -3/32
9. 9.

   f(x) = x/(x − 1) has f′(x) = -1/(x − 1)². Tala differentiates again. What is f″(4)?

   2/27
10. 10.

    f(x) = x/(x + 4) has f′(x) = 4/(x + 4)². Zee differentiates again. What is f″(1)?

    -8/125