1. Find " for y = 4 sin?(3x). 2. What is the equation of the tangent to f(x) = 3x - 5 cos(2x) at x = 0? a) 8 sin(3x) c) 12 sin(3x) cos(3x) b) 24 sin (3x) d) 24 sin(3x) cos(3x) a) y = -5x - 3 c) y = 3x - 5 b) y = -5x + 3 d) y = 3x + 5 3. If y = 4* then what is y'(1)? 4. If f (x) and g(x) are differentiable functions with values given in the chart a) 0 c) 2 In 4 below, and k(x) = f(g(x2)), then what is b) In 4 d) 8 In 4 k' (2) ? x f g f g' 1 3 4 2/3 -5/2 5. Which is the equation of the tangent to 2 4 2 4/3 -3/2 f(x) = esinx + x at x = 0? 4 8 1 8/3 1/2 a) 1/3 c) 4/3 a) y = 2x - 1 c) y = 1 b) 2/3 d) 16/3 b) y = 2x + 1 d) y =0 6. What is the slope of the line normal to the curve 7. If f (x) = 2x cos x, then f'(x) = h(x) = v5x3 - 2x + 1atx = 1? a) -2 sin x c) 2x sin x + 2 cos x a) -13/4 c) 13/4 b) -2x sin x d) -2x sinx + 2 cos x b) -4/13 d) 4/13 The equation of the tangent to the function 9. If f (x) = cos(ex), then f'(x) = y = 8v3x + 1at x = 5 is a) sin (e2x) c) -2sin (e2x) a) y = 3x + 17 c) y = 6x + 12 b) 2sin (e2x) d) -2ex sin (e2x) b) y = x+ 27 d) y = 6x + 210. If f (x) = tan (3x), then f' (=) = 11. Let f (x) = 2esx and g(x) = 5x3. At what value of x do the graphs of f and g have a) 4/3 c) 12 parallel tangent lines? b ) 4 d) 6V/3 a) -0.445 c) -0.251 b) -0.366 d) -0.165 12. If f(x) = xv4x - I then f'(x) = 13. [cos3(x7)] = V4X-1 C) -6.x+2 a) 6.x-1 V4X-1 a) 6x cos? (x2) c) -3sin (x2) cos?(x2) 2x b) - VAX-1 d) 9x-2 2V4x-1 b) sin3(x2) d) -6x sin(x2) cos2(x2) 14. An equation of the tangent line to the graph of 15. If f (x) = = then f'(x) = y = cos(3x) at x = = is a) y = 3 (x -=) c) y = - (x - = ) a) 1 c) e (3x+1) 3x2 b ) y = - 3(x - =) d) y = -2(x -#) +1 b) e3x d) es(3x-1) 3x2 16. Let f(x) = 5e3x. For what positive value of a is the 17. Let f(x) = v2x. If the rate of change slope of the line tangent to f at (a, f(a)) equal to 6? of f at x = c is four times the rate of change at x = 1, then c = ? a) 0.142 c) 0.595 b) 0.344 d) 0.714 a) 1/16 c) 1 b) 1/(2V/2) d) 3218. If f (x) = (In x)6 find f'(x). 6 (Inx)5 a) c) 2 x5 19. If y = 43* find y'. b) d) In(6x5) a) 3x(4) 2x c) 123x (In 4) 123x b) In 4 d) 43x (3) (In 4) 20. If y = In vx2 - 16 find x 21. Find the derivative of the function f(x) = 2x dx Vx3-1 4-2 a C) a) 4x- Vx3 - 1 Y2-16 2vx2-16 C) x3-1 2x 2x -x3-2 x +1 b) d) b) X2-16 X2-16 V(x3-1)3 d) (x3-1)3