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Excalidraw Data
Text Elements
g(x)f’(x) - f(x)g’(x)
g((x))^2
g(5)f’(5) - f(5)g’(5)
g(5)^2
-3(1) - 10(8) -3 - 80 -83 / -3^2 -83 / -9
product rule
f’(x)g(x)+f(x)g’(x) 4x^3(-9x-9) + x^4(-9) 4x^3(-9x-9) -9x^4 -36x^4 -36x^3 -9x^4 -45x^4 -36x^3
(-7x^2 + 7)(-2x+4) f’(x)g(x)+f(x)g’(x)
-14x(-2x+4) + (-7x^2+7)(-2) 28x^2 - 56x + 14x^2 -14 42x^2 -56x -14
(-2x^(-2)-7)(-x-3) (4x^(-3))(-x-3) + (-2x^(-2)-7)(-1) -4x^-2 -12x^-3 + 2x^(-2)+7 -2x^-2 -12x^-3 +7
quotient rule (f’(x)g(x) - f(x)g’(x))/(g(x)^2)
f/g
(-8)(4x+3)-(-8x)(4) -32x-24+32x -24/(4x+3)(4x+3)
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(4x^3)(5x^3+6)-(x^4-9)(15x^2) 20x^6+24x^3-(15x^6-135x^2) 20x^6+24x^3-15x^6+135x^2 (5x^6+24x^3+135x^2)/(5x^3+6)(5x^3+6)
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(8x)(5x-2) - (5)(4x^2) 40x^2-16x -20x^2 (20x^2-16x)/(5x-2)(5x-2) 4x(5x-4)/(5x-2)(5x-2)
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(21x^6+12x^2)(5x^3-9) - (3x^7+4x^3)(15x^2) (105x^9-189x^6+60x^5-108x^2) - (45x^9+60x^5) 105x^9-189x^6+60x^5-108x^2 - 45x^9 - 60x^5 (60x^9-189x^6-108x^2)/(5x^3)(5x^3)
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
2sqrt(x) / 2x+7
2x^(1/2) / 2x+7
(x^-1/2)(2x+7)-(2x^(1/2)(2) 2x^(1/2) + 7x^(-1/2) - 4x^(1/2) -2x^(1/2) + 7x^(-1/2) / (2x+7)
(x^(-1/2))(-2x+7)/(2x+7)
(1-2sqrt(x))/(4x^4+1) (1-2x^-1)/(4x^4+4) (f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(-x^-1/2)(4x^4+1) - (1-2x^1/2)(16x^3) -4x^(7/2) -x^(-1/2) -(16x^3-32x^7/2) -4x^(7/2) -x^(-1/2) -16x^3+32x^7/2 28x^(7/2) -16x^3 -x^(-1/2)
(28x^(7/2) -16x^3 -x^(-1/2))/(4x^4+1)^2
f’(x)g(x)+f(x)g’(x) (-13)(4)+(7)(-1) -52-7 -59
(g’(x)f(x) - g(x)f’(x))/(f(x)^2)
(8)(-3) - (-3)(9) -24 +27 3
-3^2 = 9
3/9 1/3
f’(x)g(x)+f(x)g’(x) (-2)(-3x+2) + (-2x-2)(-3) 6x-4 + (6x+6) 6x-4+6x+6 12x+2
12x+2=0 12x=-2 x=-2/12 x=-1/6
f(-1/6) (-2(-1/6)-2)(-3(-1/6)+2) (1/3-2)(1/2+2) 1/6 + 2/3 - 1 - 4 1/6 + 4/6 - 6/6 - 24/6 -25/6
(-1/6, -25/6)
f’(x)g(x)+f(x)g’(x) (.87)(.87x+80) + (.87x + 40)(.87) .7569x+69.6 + .7569x + 34.8 1.5138x + 104.4
1.5138(91) + 104.4 137.7558 + 104.4 242.1558 242.16
(8 + 1/t)(t^2 + 1/9) (8 + t^-1)(t^2 + 1/9)
f’(x)g(x)+f(x)g’(x) (-t^-2)(t^2+1/9) + (8 + t^-1)(2t) -1 - 1/9t^-2 + 16t + 2 -1/9t^-2 + 16t +1
f’(x)g(x)+f(x)g’(x) (-2x)(-5x^2+3x-4) + (-x^2-3)(-10x+3) 10x^3-6x^2+8x + 10x^3 -3x^2 +30x -9 20x^3 -9x^2 + 38x -9
20(-1)^3 -9(-1)^2 +38(-1) -9 20(-1) -9 - 38 - 9 -20 -9 - 38 -9 -76
-76(-1) = 76 48 - 76 = -28
-76x-28
f’(x)g(x)+f(x)g’(x) (2x)(-10x^4-10) + (x^2)(-40x^3) -20x^5 -20x + -40x^5 -60x^5 - 20x
f’(x)g(x)+f(x)g’(x) (-35x^4)(-4x^3-8) + (-7x^5+8)(-12x^2) 140x^7 + 280x^4 + 84x^7 -96x^2 84x^7 + 140x^7 -96x^2 + 280x^4 224x^7 + 280x^4 - 96x^2
f’(x)g(x)+f(x)g’(x) (2x^-3)(3x^3+6) + (-(x^-2)-3)(9x^2) 6x^0 + 12x^-3 + -9x^0 - 27x^2 6 + 12x^-3 -9 -27x^2 -27x^2 + 12^-3 -3
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
((-8)(x+7) - (-8x)(1))/(x+7)^2 (-8x-56 + 8x)/(x+7)^2 -56/(x+7)^2
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
((4x^3)(5x^3+6) - (x^4-9)(15x^2))/(5x^3+6)^2 (20x^6+24x^3 - 15x^6 + 135x^2)/(5x^3+6)^2 (5x^6+24x^3 + 135x^2)/(5x^3+6)^2
2/x + 3x^4 -7x^5
2x^-1 +3x^4 -7x^5 -2x^-2 + 12x^3 -35x^4
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(4x)(3x-2) - (2x^2)(3) 12x^2 -8x - 6x^2 (6x^2 -8x) / (3x - 2)^2 2x(3x -4) / (3x-2)^2
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(32x^7)(5x^7-7) - (4x^8+6)(35x^6) 160x^14 -224x^7 -140x^14 - 210x^6 20x^14 -224x^7 -210x
(20x^14 -224x^7 -210x^6)/(5x^7-7)
(f’(x)g(x) - f(x)g’(x))/(g(x)^2)
(t^-1/2)(3t+2) - (2t^1/2)(3) 3t^1/2+2(t^-1/2) - 6(t^1/2) -3t^1/2 +2t^-1/2
(-3t^1/2 +2t^-1/2)/(3t+2)^2
(f’(x)g(x) - f(x)g’(x))/(g(x)^2) (-6u^2)(2u^(1/2)+9) - (1-2u^3)(u^(-1/2)) -12u^5/2 -54u^2 - (u^(-1/2)+2u^(5/2)) -54u^2 -12u^5/2 - u^(-1/2) - 2u^(5/2) -54u^2 -10u^5/2 - u^(-1/2) (-10u^5/2 -54u^2 - u^(-1/2))/(2u^(1/2) + 9)^2
f’(x)g(x)+f(x)g’(x)
(2)(4) + (3)(5) 8 + 15 23
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