12th grade Second and higher derivatives worksheet

Second and higher derivatives

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)?
2. 2.

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

   Esme differentiates f(x) = (-2x + 5)³ twice with the chain rule. What is f″(1)?
4. 4.

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

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

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

   Luz differentiates f(x) = x²eˣ twice. Which is f″(x)?

   • f″(x) = (x² + 4x + 2)eˣ
   • f″(x) = x²eˣ
   • f″(x) = (x² + 2x)eˣ
   • f″(x) = (x² + 2x + 2)eˣ
7. 7.

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

   • f″(x) = −1/x
   • f″(x) = ln x + 1
   • f″(x) = 0
   • f″(x) = 1/x
8. 8.

   f(x) = x/(x + 1) has f′(x) = 1/(x + 1)². Pia differentiates again. What is f″(2)?
9. 9.

   f(x) = x/(x + 3) has f′(x) = 3/(x + 3)². Ren differentiates again. What is f″(1)?
10. 10.

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