2.3

1. g(x)=(x^2+1)(x^2-2x) = (x^2 +1)(2x-2)+(x^2-2x)(2x) =2x^3-2x^2+2x-2+2x^3-4x^2 =4x^3-6x^2+2x-2 =2(2x^3-3x^2+x-1) Worked by Brooke Elias CORRECT! Checked by Olga Tobias

7. f(x)= (x)/(x^2+1) =[(x^2+1)(1)-(x)(2x)]/[(x^2+1)^2] =(1-x^2)/[(x^2+1)^2] Worked by Brooke Elias CORRECT!! Checked by Olga Tobias :)

13. Worked by Nadia Guillen: f(x)= (x^3-3x)(2x^2+3x+5); c=0 f'(x)=(3x^2-3)+(4x+3) f'(x)=3x^2-4x f'(0)=0

Correct- Checked by Warner Boin

17. f(x)=xcosx c=pie/4 f ' (x)=(1)(cosx)+(-sinx)(x) f ' (x)=cosx-xsinx f ' (pie/4)=cos(pie/4)-(pie/4)sin(pie/4) f ' (pie/4)=((root 2)/2)-(pie/4)((root 2)/2) f ' (pie/4)=((root 2)/8)(4-pie) worked by Ellen Wagner

19.y=(x^2+2x)/3 y=(1/3)(x^2+2x) y' =(1/3)(2x+2) y' =(2(x+1))/3 worked by Ellen Wagner 17 and 19 correct checked by Louis Ortiz....

31. h(s)= (s^3 -2)^2 h(s)= 2(s^3 -2)[d(s^3 -2)] h(s)=2(s^3 -2)[d(s^3) + d(-2)] h(s)=2(s^3 -2)[3s^2 + 0] h(s)=6s^2(s^3 -2) worked by Will Owen

Correct! Checked by Brooke Elias
 * 1) 21 and #25. Worked by Olga Tobias



37. (x^2-c^2)(2x)-(x^2+c^2)(2x)/(x^2-c^2)^2 = -4xc^2/(x^2-c^2)^2

39. t^2sint= (t^2)(cos t) + sin t(2t) = t(t cos t + 2 sin t) Worked by: Anthony Lukefahr Checked by: Jackson <3 (Hart)

55) ((x+1)/(x+2))(2)+(2x-5)[((x+2)(1)-(x+1)(1))/(x+2)^2]=(2x^2+8x-1)/(x+2)^2 Worked by Kendall Jones Checked by Kara Manning

59.) y= 1+cscx/ 1-cscx Pt. (pi/6, -3)

y1=(1-cscx)(-cscxcotx)-(1+cscx)(cscxcotx)

(1-cscx)^2 =-2cscxcotx/(1-cscx)^2 y1=-2(2)(square root of 3)/(1-2)^2 =-4 square root of 3 Worked By: Abby Newton (sorry for the long line... it's a fraction)

69. f(x)=8/x^2+4 f'(x)=16x m=32 y-1=32(x-2) worked by Alex Stevens Checked by Elborz Safarzadeh: Wrong Answer Correct answer is 2y+x-4=0

73.) f(x)= x^2/(x-1) =(x-1)(2x)-(x^2)(1)/ (x-1)^2 =2x^2-2x-x^2/ (x-1)^2 =x^2-2x/ (x-1)^2 =x(x-2)/(x-1)^2

f1(0)= 0(-2)/(-1)^2 =0 f1(2)=2(0)/(-1)^2 =0 x=0,2 Horizontal Tangents at (0,0) and (2,4) Worked by: Abby Newton Correct! Checked by Michelle Tassin

83. f(x)=2t+1 g(x)= root t

2t+1(1/2t^-1/2)+2(root t)= 2t+1(1/2root t)+ 2root t= 2 root t ((2t+1/2 root t) + 2 root t) 2t+1+4t= 6t + 1 (2 root t) (6t+1)(2root t) cm2/sec worked by hyun bang

93. f(x)= 4x^(3/2) =3/ sqrt. x 97. f(x)= 3sinx = -3 sinx 93 and 97 worked by emily othold

99. f'(x)=x^2 find, f''(x) =2x^1 =2x f''(x)=2x

101. f'''(x)=2rootx find f^(4)(x) =2*x^(1/2) =2*1/2*x^(-1/2) =x^(-1/2) =1/(x^(1/2)) f^(4) x))= 1/(x^(1/2))

99&101 worked by sheridan gabrisch both correct! checked by Morgan Clinkscales

105. f (x)= 2g(x) + h(x) f '(2)= 2g'(2) + h'(2) f '(2)= 2(-2) + 4 f '(2)= -4 + 4 f '(2)= 0 106. f (x)= 4 - h(x) f '(2)= 4 - h'(2) f '(2)= 4- 4 f '(2)= 0 105 & 106 Checked by Chasitey Ureste
 * 1) 105 - 106 worked by Samantha Cuestas