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submit work for problems 3 11 and 17
1/x + 4x^5 -2x^6 -2x^6 + 4x^5 + 1/x
-2x^6 + 4x^5 + 1/x -2x^6 + 4x^5 + x^-1 -12x^5 + 20x^4 + x^-2 -12x^5 + 20x^4 + 1/x^2
problem 3:
f’g + fg’
(3x+7)(-3x^3-4) f = 3x+7 g = -3x^3 - 4
f’ = 3 g’ = -9x
3(-3x^3-4) + (3x+7)(-9x^2) -9x^3-12 + -27x^3 - 63x^2 -36x^3 -63x^2 -12
6t/(t+4)
(f’g - fg’) / g
f = 6t g = t+4
f’ = 6 g’ = 1
(6(t+4) - 6t(1)) / (t+4)^2 (6t+24-6t)/(t+4)^2 24/(t+4)^2
f’g + fg’
f = 13 g = 7
f’ = 10 g’ = -12
10(7) + 13(-12) 70 -156 -86
f’(g(x)) * g’(x)
f = x^4 g = 2-3x
f’ = 4x^3 g’ = -3
4(2-3x)^3 * -3 -12(2-3x)^3
f’(g(x)) * g’(x)
f = cbrt(x) g = 8x
f’ = (1/3)x^(-2/3) g’ = 16x
(8x^2-7)^(-2/3) * 16x (16x/3)(8x^2-7)^(-2/3)
f’(g(x)) * g’(x)
f = x^(3/2) g = -3x^-3 + 2x + 4
f’ = 3/2x^(1/2) g’ = 9x^-4 + 2
3/2(-3x^-3+2x+4)^(1/2) * (9x^-4+2)
.7x^3 + 9xy + 7.1y^3 = 117760.5 2.1x^2 + 9(dy/dx) + 21.3y^2(dy/dx) = 0 9(dy/dx) + 21.3y^2(dy/dx) = -2.1x^2 (dy/dx)(9+21.3y^2) = -2.1x^2 dy/dx = (-2.1x^2)/(9+21.3y^2)
.7x^3 + 9xy + 7.1y^3 = 117760.5
9xy f’g + fg’ f = 9x g = y
f’ = 9 g’ = (dy/dx)
9y + 9x(dy/dx)
2.1x^2 + 9y + 9x(dy/dx) + 21.3y^2(dy/dx) = 0 9x(dy/dx) + 21.3y^2(dy/dx) = -2.1x^2 -9y (dy/dx)(9x+21.3y^2) = -2.1x^2 -9y dy/dx = (-2.1x^2-9y)/(9x+21.3y^2)
(-2.1(27)^2-9(24))/(9(27)+21.3(24)^2) (-2.1(729) -216)/(243+21.3(576)) (-1530.9-216)/(243+12268.8) (-1746.9)/(12511.8) -.1396 -.140
2x^3-2xy-3y^3 = 5
-2xy f’g + fg’
f = -2x g = y
f’ = -2 g’ = dy/dx
-2y + -2x(dy/dx)
6x^2-2y -2x(dy/dx) -9y^2(dy/dx) = 0
-2x(dy/dx) -9y^2(dy/dx) = 2y-6x^2 (dy/dx)(-2x-9y^2) = 2y-6x^2 dy/dx = 2y-6x^2/(-2x-9y^2) dy/dx = 6x^2-2y/(2x+9y^2)
3x^4+5y^3 = 8 12x^3(dx/dt) + 15y^2(dy/dt) = 0 12x^3(dx/dt) = -15y^2(dy/dt) 12x^3/(-15y^2) * dx/dt = dy/dt -4x^3/5y^2 * dx/dt = dy/dt
problem 11
area of rectangle = l*w
l’ = 5 w’ = -4
l = 75 w = 65
rate of change of area: l’w + lw’ 565 + 75-4 325 - 300 25
3112
4ft/s
1512
x
a^2 + b^2 = c
1512^2 + b^2 = 3112^2 2286144 + b^2 = 9684544 b^2 = 7398400 b = 2720
c = 3112 b is increasing by 4/s b’ = 4
a^2 + b^2 = c^2 rateofchange = 2a + 2b = 2c 2x + 2(4) = 0
4ft/s moving down the wall.
2720
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