1. Differentiation
Given the information about differentiable functions f(x) and g(x), determine the value.

2. Worksheet a) d/dx (2 f(x) ) at x = 2 2 • f ’ (2) = 2 • (1/3) = 2/3
b) d/dx( f(x) + g(x) ) at x = 3
f ’ (3) + g ’ (3) = 2 + 5
c) d/dx ( f(x) • g(x) ) at x = 3
f(3) • g’(3) + g(3) • f’(3) =
3 • 5 + (-4) • 2  =
15 - 8

3. Worksheet
d/dx (f(x) / g(x)) at x = 2

4. Worksheet d/dx (f(g(x)) at x = 2
f ’ (g(2)) • g’ (2) = f ’ (2) • g’ (2)
= 1/3 • - 3
= -1

5. Worksheet f)

6. = -1/(-4)2 • 5 = -5/16 Worksheet d/dx ( 1/g(x) ) at x = 3
d/dx ( g(3)) -1 = -1 (g(3)) -2 • g’(3)
= -1/(-4)2 • 5
= /16

7. Worksheet h)

8. Worksheet h)

9. Worksheet h)

10. Worksheet

11. Worksheet

12. Worksheet

13. #2

14. #3 , 4 3. None x = 0 x = 0, x≤0 Corner points Cusp, Discontinuous
Vertical tangent