Inverse function rule and inverse trig derivatives

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   At x = 1, 3 and 6; at x = 3, 10 and 2. f has an inverse g. Bo uses the table shown. What is g′(3)?

   1/6
2. 2.

   At x = 0, 4 and -2; at x = 4, 7 and 5. f has an inverse g. Esme uses the table shown. What is g′(4)?

   -1/2
3. 3.

   At x = 3, 8 and 5; at x = 8, 1 and -4. f has an inverse g. Jun uses the table shown. What is g′(8)?

   1/5
4. 4.

   Kira differentiates f(x) = 3 arcsin x. Which is f′(x)?

   • f′(x) = 3/√(1 + x²)
   • f′(x) = −3/√(1 − x²)
   • f′(x) = 3/√(1 − x²)
   • f′(x) = 3/(1 + x²)
5. 5.

   Luz differentiates f(x) = 2 arccos x. Which is f′(x)?

   • f′(x) = −2/√(1 − x²)
   • f′(x) = 2/√(1 − x²)
   • f′(x) = −2/(1 + x²)
   • f′(x) = −2/√(1 + x²)
6. 6.

   Milo differentiates f(x) = 5 arctan x. Which is f′(x)?

   • f′(x) = 5/(1 + x²)
   • f′(x) = 5/(1 − x²)
   • f′(x) = −5/(1 + x²)
   • f′(x) = 5/√(1 − x²)
7. 7.

   Pia differentiates f(x) = 10 arctan x. What is f′(3)?

   1
8. 8.

   Ren differentiates f(x) = 15 arctan x. What is f′(2)?

   3
9. 9.

   Tala differentiates f(x) = 8 arctan x. What is f′(-3)?

   4/5
10. 10.

    Zee differentiates f(x) = 34 arctan x. What is f′(4)?

    2