Составьте и розвяжите уравнения f'(x)= g'(x),если f(x)=(2x-1)^5, g(x)=10x+7.
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Ответил nafanya2014
0
f`(x)=((2x-1)⁵)`=5(2x-1)⁴,
g`(x)=(10x+7)`=10
f`(x)=g`(x)
5(2x-1)⁴=10
(2x-1)⁴=2
![2x-1= sqrt[4]{2}](https://tex.z-dn.net/?f=2x-1%3D+sqrt%5B4%5D%7B2%7D+ "2x-1= sqrt[4]{2}")
или ![2x-1= -sqrt[4]{2}](https://tex.z-dn.net/?f=2x-1%3D+-sqrt%5B4%5D%7B2%7D+ "2x-1= -sqrt[4]{2}")
![2x=1+ sqrt[4]{2}](https://tex.z-dn.net/?f=2x%3D1%2B+sqrt%5B4%5D%7B2%7D "2x=1+ sqrt[4]{2}")
или ![2x=1-sqrt[4]{2}](https://tex.z-dn.net/?f=2x%3D1-sqrt%5B4%5D%7B2%7D "2x=1-sqrt[4]{2}")
![x= frac{1+ sqrt[4]{2} }{2}](https://tex.z-dn.net/?f=x%3D+frac%7B1%2B+sqrt%5B4%5D%7B2%7D+%7D%7B2%7D+ "x= frac{1+ sqrt[4]{2} }{2}")
или ![x= frac{1- sqrt[4]{2} }{2}](https://tex.z-dn.net/?f=x%3D+frac%7B1-+sqrt%5B4%5D%7B2%7D+%7D%7B2%7D "x= frac{1- sqrt[4]{2} }{2}")
g`(x)=(10x+7)`=10
f`(x)=g`(x)
5(2x-1)⁴=10
(2x-1)⁴=2
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