Inverse function rule and inverse trig derivatives

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   f(x) = x³ + 2x + 1 has an inverse g, and f(1) = 4. Ari finds g′(4). What is it?

   1/5
2. 2.

   f(x) = x³ + 4x − 3 has an inverse g, and f(1) = 2. Bo finds g′(2). What is it?

   1/7
3. 3.

   f(x) = x³ + 3x + 5 has an inverse g, and f(2) = 19. Esme finds g′(19). What is it?

   1/15
4. 4.

   Luz uses the chain rule on f(x) = arcsin(3x). What is f′(0.2)?

   3.75
5. 5.

   Milo uses the chain rule on f(x) = arcsin(5x). What is f′(0.12)?

   6.25
6. 6.

   Noah uses the chain rule on f(x) = arcsin(4x). What is f′(0.15)?

   5
7. 7.

   Pia uses the chain rule on h(x) = arctan(x²). Which is h′(x)?

   • h′(x) = −2x/(1 + x⁴)
   • h′(x) = 1/(1 + x⁴)
   • h′(x) = 2x/(1 + x⁴)
   • h′(x) = 2x/(1 + x²)
8. 8.

   Ren uses the chain rule on h(x) = arcsin(3x). Which is h′(x)?

   • h′(x) = 3/√(1 − 3x²)
   • h′(x) = 1/√(1 − 9x²)
   • h′(x) = −3/√(1 − 9x²)
   • h′(x) = 3/√(1 − 9x²)
9. 9.

   Tala uses the chain rule on h(x) = arctan(eˣ). Which is h′(x)?

   • h′(x) = −eˣ/(1 + e^(2x))
   • h′(x) = eˣ/(1 + eˣ)
   • h′(x) = eˣ/(1 + e^(2x))
   • h′(x) = 1/(1 + e^(2x))
10. 10.

    Zee uses the chain rule on h(x) = arccos(√x). Which is h′(x)?

    • h′(x) = −1/√(1 − x)
    • h′(x) = 1/(2√x √(1 − x))
    • h′(x) = −1/(2√x √(1 − √x))
    • h′(x) = −1/(2√x √(1 − x))