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Danil12345qw
@Danil12345qw
May 2022
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Помогите решить примеры по теме - производная элементарных функций
Срочно!!!пж
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Answers & Comments
1.![y' = -3*4x^3+\frac{16}{2\sqrt{x} } + \frac{4}{x^2} = -12x^3+\frac{8}{\sqrt{x} } + \frac{4}{x^2} y' = -3*4x^3+\frac{16}{2\sqrt{x} } + \frac{4}{x^2} = -12x^3+\frac{8}{\sqrt{x} } + \frac{4}{x^2}](https://tex.z-dn.net/?f=y%27%20%3D%20-3%2A4x%5E3%2B%5Cfrac%7B16%7D%7B2%5Csqrt%7Bx%7D%20%7D%20%2B%20%5Cfrac%7B4%7D%7Bx%5E2%7D%20%3D%20-12x%5E3%2B%5Cfrac%7B8%7D%7B%5Csqrt%7Bx%7D%20%7D%20%2B%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
2.![y' = (e^x+4x)(1+3x)+(e^x+2x^2)3 = e^x+3xe^x+4x+12x^2+3e^x+6x^2 = 4e^x+3xe^x+18e^x+4x y' = (e^x+4x)(1+3x)+(e^x+2x^2)3 = e^x+3xe^x+4x+12x^2+3e^x+6x^2 = 4e^x+3xe^x+18e^x+4x](https://tex.z-dn.net/?f=y%27%20%3D%20%28e%5Ex%2B4x%29%281%2B3x%29%2B%28e%5Ex%2B2x%5E2%293%20%3D%20e%5Ex%2B3xe%5Ex%2B4x%2B12x%5E2%2B3e%5Ex%2B6x%5E2%20%3D%204e%5Ex%2B3xe%5Ex%2B18e%5Ex%2B4x)
3.![y' = (14x-4)(2-6x)+(7x^2-4x+1)(-6) = 28x-84x^2-8+24x-42x^2+24x-6 = 126x^2+76x-14 y' = (14x-4)(2-6x)+(7x^2-4x+1)(-6) = 28x-84x^2-8+24x-42x^2+24x-6 = 126x^2+76x-14](https://tex.z-dn.net/?f=y%27%20%3D%20%2814x-4%29%282-6x%29%2B%287x%5E2-4x%2B1%29%28-6%29%20%3D%2028x-84x%5E2-8%2B24x-42x%5E2%2B24x-6%20%3D%20126x%5E2%2B76x-14)
4.![y' = \frac{5(3x^2+1)-(5x-1)*6x}{(3x^2+1)^2} = \frac{15x^2+5-30x^2+6x}{(3x^2+1)^2} = \frac{-15x^2+6x+5}{(3x^2+1)^2} y' = \frac{5(3x^2+1)-(5x-1)*6x}{(3x^2+1)^2} = \frac{15x^2+5-30x^2+6x}{(3x^2+1)^2} = \frac{-15x^2+6x+5}{(3x^2+1)^2}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B5%283x%5E2%2B1%29-%285x-1%29%2A6x%7D%7B%283x%5E2%2B1%29%5E2%7D%20%3D%20%5Cfrac%7B15x%5E2%2B5-30x%5E2%2B6x%7D%7B%283x%5E2%2B1%29%5E2%7D%20%3D%20%5Cfrac%7B-15x%5E2%2B6x%2B5%7D%7B%283x%5E2%2B1%29%5E2%7D)
5.![y' = x^2-2x\\y'(-2) = (-2)^2-2*(-2) = 4+4=8 y' = x^2-2x\\y'(-2) = (-2)^2-2*(-2) = 4+4=8](https://tex.z-dn.net/?f=y%27%20%3D%20x%5E2-2x%5C%5Cy%27%28-2%29%20%3D%20%28-2%29%5E2-2%2A%28-2%29%20%3D%204%2B4%3D8)