Inverse function rule and inverse trig derivatives

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   f(x) = x + eˣ is always increasing, so it has an inverse g. Ari finds g′(1). What is it?

   0.5
2. 2.

   f(x) = x⁵ + x³ + x is always increasing, so it has an inverse g. Bo finds g′(3). What is it?

   1/9
3. 3.

   f(x) = x³ + 4x − 2 is always increasing, so it has an inverse g. Esme finds g′(3). What is it?

   1/7
4. 4.

   f(x) = x³ + 2x is always increasing, so it has an inverse g. Jun finds g′(-3). What is it?

   1/5
5. 5.

   A camera 300 m from a launch pad tracks a rocket rising 250 m/s, at angle θ = arctan(h/300). Kira finds dθ/dt at h = 400. What is it, in radians per second?

   3/10
6. 6.

   A sensor 30 m from a pole tracks a kite climbing it at 10 m/s, at angle θ = arctan(h/30). Luz finds dθ/dt at h = 40. What is it, in radians per second?

   3/25
7. 7.

   A lamp 8 m from a wall lights a balloon rising 3 m/s, at angle θ = arctan(h/8). Noah finds dθ/dt at h = 6. What is it, in radians per second?

   6/25
8. 8.

   Pia wants the exact slope of f(x) = arcsin x at x = 1/2. What is f′(1/2)?

   • f′(1/2) = 4/3
   • f′(1/2) = 2√3/3
   • f′(1/2) = −2√3/3
   • f′(1/2) = √2
9. 9.

   Ren wants the exact slope of f(x) = arccos x at x = √3/2. What is f′(√3/2)?

   • f′(√3/2) = 2
   • f′(√3/2) = −2
   • f′(√3/2) = −4
   • f′(√3/2) = −(√3 + 1)
10. 10.

    Zee wants the exact slope of f(x) = arccos x at x = 1/2. What is f′(1/2)?

    • f′(1/2) = −√2
    • f′(1/2) = 2√3/3
    • f′(1/2) = −4/3
    • f′(1/2) = −2√3/3