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5.
![y= sqrt[3]{5+4x-x^2}- frac{5}{(x+1)^3}=(5+4x-x^2)^{ frac{1}{3} }-5(x+1)^{-3} \ \
y'= frac{1}{3}(5+4x-x^2)^{- frac{2}{3} }(4-2x)-5*(-3)(x+1)^{-4}= \ \
= frac{4-2x}{3 sqrt[3]{(5+4x-x^2)^2} }+ frac{15}{(x+1)^4}](https://tex.z-dn.net/?f=y%3D+sqrt%5B3%5D%7B5%2B4x-x%5E2%7D-+frac%7B5%7D%7B%28x%2B1%29%5E3%7D%3D%285%2B4x-x%5E2%29%5E%7B+frac%7B1%7D%7B3%7D+%7D-5%28x%2B1%29%5E%7B-3%7D+%5C++%5C+%0Ay%27%3D+frac%7B1%7D%7B3%7D%285%2B4x-x%5E2%29%5E%7B-+frac%7B2%7D%7B3%7D+%7D%284-2x%29-5%2A%28-3%29%28x%2B1%29%5E%7B-4%7D%3D+%5C++%5C+%0A%3D++++frac%7B4-2x%7D%7B3+sqrt%5B3%5D%7B%285%2B4x-x%5E2%29%5E2%7D+%7D%2B+frac%7B15%7D%7B%28x%2B1%29%5E4%7D++ "y= sqrt[3]{5+4x-x^2}- frac{5}{(x+1)^3}=(5+4x-x^2)^{ frac{1}{3} }-5(x+1)^{-3} \ \
y'= frac{1}{3}(5+4x-x^2)^{- frac{2}{3} }(4-2x)-5*(-3)(x+1)^{-4}= \ \
= frac{4-2x}{3 sqrt[3]{(5+4x-x^2)^2} }+ frac{15}{(x+1)^4}")
6.
![y' =3sin^27x*7cos7x*arcctg5x^2+sin^37x* (- frac{10x}{1+5x^2} )= \ \
=21sin^27xcos7x*arcctg5x^2- frac{10xsin^37x}{1+5x^2}](https://tex.z-dn.net/?f=y%27+%3D3sin%5E27x%2A7cos7x%2Aarcctg5x%5E2%2Bsin%5E37x%2A+%28-+frac%7B10x%7D%7B1%2B5x%5E2%7D+%29%3D+%5C++%5C+%0A%3D21sin%5E27xcos7x%2Aarcctg5x%5E2-+frac%7B10xsin%5E37x%7D%7B1%2B5x%5E2%7D+ "y' =3sin^27x*7cos7x*arcctg5x^2+sin^37x* (- frac{10x}{1+5x^2} )= \ \
=21sin^27xcos7x*arcctg5x^2- frac{10xsin^37x}{1+5x^2}")
6.
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