reviewws2_math116

reviewws2_math116 - y’ =(x 3 9(x – 5(x 3(x-5 y’ =(10x...

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106 great job Math 116 Kim Peppard instructor – online -5 wrong file name 1. a. y’= (5x^6 -3x^4 +25x^3 -1)(4x -8) + (2x^2 -8x +9)(30x^5 -12x^3 +75x^2) b. outside = -15( )^-`6 inside = (10x^4 -15x^2 +1) y`= -15(2x^5 -5x^3 +x -2)^-16(10x^4 -15x^2 +1) c. y’ = (2x^2)*1/2(9-x)^-1/2 + (4x)*(9-x)^1/2 y’= (2x^2)/2(9-x)^1/2 + (4x)(9-x)^1/2 y’ = x^2/[(9-x)^1/2 + (4x)(9-x)^1/2] negative on first term d. –1 e. f. y’ = [(5x^3 +2x)^5 * 3 – (3x-1)*5(5x^3+2x)^4(15x^2+2)] /(5x^3+2x)^10 y’ = [(5x^3 +2x) * 3 – (3x-1) * 5(15x^2+2)] / (5x^3+2x)^6 2. a. outside’ = 1/(3x^4 –2x) inside ‘ = 12x^3 –2 y’ = (12x^3 –2)/(3x^4 –2x) b. y’ = [(3x – 7)/(5x^3 +2)] [(5x^3 + 2)*3 – (3x-7)*15x^2]/ (3x-7)^2 y’ = [(5x^3 + 2) * 3 – (3x – 7) * 15x^2] / [(5x^3 + 2)(3x – 7)] c. y’ = 1 / [(x+3)(x-5)^9] * {[(x+3) * 9(x-5)^8 + (x-5)^9] / [(x+3)(x-5)^9]} y’ = [(x+3) * 9(x-5)^8 + (x-5)^9] / [(x+3)(x-5)^9] / [(x+3)(x-5)^9]
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Unformatted text preview: y’ = [(x+3) * 9 + (x – 5)] / [(x+3)(x-5)] y’ = (10x + 22) / [(x+3)(x+5)] 3. a. y’ = -18e^x * 1 y’ = -18e^x b. y’ = e^(3x^2 – 5x) * (6x – 5) c. y’ = (x^8)(e^-2x * -2) + (8x^7)(e^-2x) y’ = (e^-2x * x^7)(-2x + 8) y’ = (-2x^7 * e^-2x)(x – 4) 4. a. 10x^4 – 3y^2(y’) + 3y’ = 0 3y’ – 3y^2(y’) = -10x^4 y’ = -10x^4 / (3 – 3y^2) y’ = (-10x^4 – 3y)/(-3y^2 + 3x)-7 5. a. 90x^9 – 32x^7 – 42x^5 810x^8 –224x^6 –210x^4 y’’’ = 6480x^7 –1344x^5 –840x^3 +6 b. (e^(5x^6) * 150x^4) + (e^(5x^6) * 30x^5 * 30x^5) e^(5x^6) * (150x^4 + 900x^10) 150x^4 * e^(5x^6)*(1 + 6x^6) +6 c. y’ = (x^7)(1/x) + (7x^6)(ln x) y’’ = 6x^5 + 42x^(ln x) + (1/x)(7x^6) y’’ = 6x^5 + 42x^(ln x) + 7x^5 y’’ = 13x^5 + 42x^5(ln x) +6...
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reviewws2_math116 - y’ =(x 3 9(x – 5(x 3(x-5 y’ =(10x...

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