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1.6
![y=5x^2- sqrt[3]{x^4} + frac{4}{x^3} - frac{5}{x} y=5x^2- sqrt[3]{x^4} + frac{4}{x^3} - frac{5}{x}](https://tex.z-dn.net/?f=y%3D5x%5E2-+sqrt%5B3%5D%7Bx%5E4%7D+%2B+frac%7B4%7D%7Bx%5E3%7D+-+frac%7B5%7D%7Bx%7D+)
![y=5x^2- x^{ frac{4}{3} } +4 x^{-3} - 5 x^{-1} y=5x^2- x^{ frac{4}{3} } +4 x^{-3} - 5 x^{-1}](https://tex.z-dn.net/?f=y%3D5x%5E2-++x%5E%7B+frac%7B4%7D%7B3%7D+%7D++%2B4+x%5E%7B-3%7D++-+5+x%5E%7B-1%7D+)
![y'=(5x^2- x^{ frac{4}{3} } +4 x^{-3} - 5 x^{-1} )'= y'=(5x^2- x^{ frac{4}{3} } +4 x^{-3} - 5 x^{-1} )'=](https://tex.z-dn.net/?f=y%27%3D%285x%5E2-++x%5E%7B+frac%7B4%7D%7B3%7D+%7D++%2B4+x%5E%7B-3%7D++-+5+x%5E%7B-1%7D+%29%27%3D)
![=2*5x- frac{4}{3} x^{ frac{4}{3}-1 }+4*(-3) x^{-3-1}-5*(- 1) x^{-2} = =2*5x- frac{4}{3} x^{ frac{4}{3}-1 }+4*(-3) x^{-3-1}-5*(- 1) x^{-2} =](https://tex.z-dn.net/?f=%3D2%2A5x-+frac%7B4%7D%7B3%7D+x%5E%7B+frac%7B4%7D%7B3%7D-1+%7D%2B4%2A%28-3%29+x%5E%7B-3-1%7D-5%2A%28-+1%29+x%5E%7B-2%7D+%3D)
![=10x- frac{4}{3} x^{ frac{1}{3} } -12 x^{-4}+5 x^{-2} =10x-1 frac{1}{3} sqrt[3]{x}- frac{12}{x^4}+ frac{5}{x^2} =10x- frac{4}{3} x^{ frac{1}{3} } -12 x^{-4}+5 x^{-2} =10x-1 frac{1}{3} sqrt[3]{x}- frac{12}{x^4}+ frac{5}{x^2}](https://tex.z-dn.net/?f=%3D10x-+frac%7B4%7D%7B3%7D+x%5E%7B+frac%7B1%7D%7B3%7D+%7D+-12+x%5E%7B-4%7D%2B5+x%5E%7B-2%7D+%3D10x-1+frac%7B1%7D%7B3%7D+sqrt%5B3%5D%7Bx%7D-+frac%7B12%7D%7Bx%5E4%7D%2B+frac%7B5%7D%7Bx%5E2%7D++++)
2.6
![y= sqrt{3x^4-2x^3+x} - frac{4}{(x+2)^3} y= sqrt{3x^4-2x^3+x} - frac{4}{(x+2)^3}](https://tex.z-dn.net/?f=y%3D+sqrt%7B3x%5E4-2x%5E3%2Bx%7D+-+frac%7B4%7D%7B%28x%2B2%29%5E3%7D+)
![y'=( sqrt{3x^4-2x^3+x} - frac{4}{(x+2)^3} )'= frac{1}{2 sqrt{3x^4-2x^3+x} }*(3x^4-2x^3+x)'- y'=( sqrt{3x^4-2x^3+x} - frac{4}{(x+2)^3} )'= frac{1}{2 sqrt{3x^4-2x^3+x} }*(3x^4-2x^3+x)'-](https://tex.z-dn.net/?f=y%27%3D%28+sqrt%7B3x%5E4-2x%5E3%2Bx%7D+-+frac%7B4%7D%7B%28x%2B2%29%5E3%7D+%29%27%3D+frac%7B1%7D%7B2+sqrt%7B3x%5E4-2x%5E3%2Bx%7D+%7D%2A%283x%5E4-2x%5E3%2Bx%29%27-)
![-4* (x+2)^{-3}= frac{1}{2 sqrt{3x^4-2x^3+x} }*(12x^3-6x^2+1)-4*(-3)* (x+2)^{-4}= -4* (x+2)^{-3}= frac{1}{2 sqrt{3x^4-2x^3+x} }*(12x^3-6x^2+1)-4*(-3)* (x+2)^{-4}=](https://tex.z-dn.net/?f=-4%2A+%28x%2B2%29%5E%7B-3%7D%3D+frac%7B1%7D%7B2+sqrt%7B3x%5E4-2x%5E3%2Bx%7D+%7D%2A%2812x%5E3-6x%5E2%2B1%29-4%2A%28-3%29%2A+%28x%2B2%29%5E%7B-4%7D%3D)
![=frac{12x^3-6x^2+1}{2 sqrt{3x^4-2x^3+x} }+12* (x+2)^{-4}=frac{12x^3-6x^2+1}{2 sqrt{3x^4-2x^3+x} }+ frac{12}{(x+2)^4} =frac{12x^3-6x^2+1}{2 sqrt{3x^4-2x^3+x} }+12* (x+2)^{-4}=frac{12x^3-6x^2+1}{2 sqrt{3x^4-2x^3+x} }+ frac{12}{(x+2)^4}](https://tex.z-dn.net/?f=%3Dfrac%7B12x%5E3-6x%5E2%2B1%7D%7B2+sqrt%7B3x%5E4-2x%5E3%2Bx%7D+%7D%2B12%2A+%28x%2B2%29%5E%7B-4%7D%3Dfrac%7B12x%5E3-6x%5E2%2B1%7D%7B2+sqrt%7B3x%5E4-2x%5E3%2Bx%7D+%7D%2B+frac%7B12%7D%7B%28x%2B2%29%5E4%7D)
2.6
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