2.4 D Worksheet Chain Rule with Tables & Graphs Name: X -3 2 7 8 g(x) 3 2 h(x) 7 -2 g'(x) -1 5 2 8 h'(x) -1 7 -3 -5 Selected values of the differentiable functions g and h along with their derivatives g' and h' are given in the table above. Use this information to find the following values. 1. Let f(x) = g(h(x)). Write an equation of the line tangent to f at x = -3. 2. Let k(x) = g(x3). Find k' (2). 3. Let m(x) = h(x) 5x . Find m' (7). 4. Let p(x) = h(g(x)). Find p'(8). 5. Let r(x) = Ing(x)|. Find r'(-3). 6. Let L(x) = eh(x). Find L'(8). 7. Let A(x) = h(1 + x - x3). Find A'(-2).8. Let n(x) = sin(g(x)) . Find n'(2). 1 9. Let D(x) = h(x) Find D'(7). f (x) -1 9 8 10 12 12 13 The graphs of f (x) and g(x) are shown in the figure above and consist of line segments. Use the graphs to answer the following 10. Let h(x) = f(g(x)). Find h'(5). 11. Let k(x) = f(x2). Find k'(-2). 12. Let p(x) = In(g(x)). Findp'(-4). 13. Let m(x) = vf(x). Find m'(-3).The graphs of f (x) and g(x) are shown in the figure above and consist of line segments. Use the graphs to answer the following. 10. Let h(x) = f(g(x)). Find h'(5). 11. Let k(x) = f(x ). Find k'(-2). 12. Let p(x) = In(g(x)) . Find p'(-4). 13. Let m(x) = vf(x). Find m'(-3). 3 14. Let A(x) = g(f(x)). Find A'(2). 15. Let C(x) = . Find C'(-4). g(x) 16. Let S(x) = ef(x). Find S'(11). 17. Let Q(x) = cos(g(x)) . Find Q' (3). 18. Let D(x) = g(2x - x2). Find D'(-1). 19. Let n(x) = InIf(x) - 3x|. Find n'(-4)