Question

Express your answer as an integer, or as a fraction in lowest terms if necessary.

1. If g(x) = - 3 f(x),   where f(6) = 10 and f'(6) = - 4,   find g'(6).

2. If g(x) = 5 x + 6 f(x), where f(- 5) = 3 and f'(- 5) = - 10, find g'(- 5).

3. If f(x) = (e^x) / x , find f'(1).

4. If f(x) = - sin x sec x,   find f'(0).

5. If h(x) =   3x f(x) - 11 g(x), where   f(2) = 15,   g(2) = 12,   f'(2) = 4, and   g'(2) = 6, find h'(2).

6. If h(x) = f(x) g(x), where f(1) = 3,   g(1) = - 5,   f'(1) = 7,   and   g'(1) = 10, find h'(1).

7. If h(x) = [f(x)] / [g(x)], where f(- 3) = - 2,   g(- 3) = 3,   f'(- 3) = 6, and   g'(- 3) = - 9, find   h'(- 3).

8. If g(x) = 1 / [f(x)], where   f(3) = 4 and   f'(3) = - 3, find   g'(3).

9. If h(x) = f(x) + [g(x)]^2,   where f(- 7) = 6, g(- 7) = 5, f'(- 7) = - 2, and g'(- 7) = - 4, find   h'(- 7).

10. If   h(x) = f (g(x)), where f(0) = 7,   g(0) = - 1,   f'(0) = 0,   g'(0) = - 3,   f(- 1) = - 3,   g(- 1) = 2,   f'(- 1) = - 5, and   g'(- 1) = 4, find h'(0).

Answer 1

1)

put x = 6,

2)

put x = -5,

3)

put x = 1,

4)

put x = 0,