Найти производную функции_а) y = (2-3x)^7б) y= (x^2 - 4x+1)^4в) y = 1/V3x+1г) y= sin ( 2x-п/6)д) y = x * e^2x-1e) y = ln (3 + Vx). Created by kirillpolev123. algebra-ru

6)д) y = x * e^2x-1e) y = ln (3 + Vx)...

July 2022 1 20 Report

Найти производную функции_
а) y = (2-3x)^7
б) y= (x^2 - 4x+1)^4
в) y = 1/V3x+1
г) y= sin ( 2x-п/6)
д) y = x * e^2x-1
e) y = ln (3 + Vx)

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NNNLLL54

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$y=(2-3x)^7\\y`=7(2-3x)^6(2-3x)`=7(2-3x)^6\cdot (-3)=-21(2-3x)^6\\2)y=(x^2-4x+1)^4\\y`=4(x^2-4x+1)^3(x^2-4x+1)`=4(2x-4)(x^2-2x+1)^3\\3) y=\frac{1}{\sqrt{3x+1}}\\y`=\frac{-1\cdot (\sqrt{3x+1})`}{(\sqrt{3x+1})^2}=\frac{-\frac{(3x+1)`}{2\sqrt{3x+1}}}{3x+1}=-\frac{3}{2\sqrt{(3x+1)^3}}\\4)y=sin(2x-\frac{\pi}{6})\\y`=cos(2x-\frac{\pi}{6})\cdot (2x-\frac{\pi}{6})`=2sin(2x-\frac{\pi}{6})\\5) y=xe^{2x-1}\\y`=1\cdot e^{2x-1}+xe^{2x-1}(2x-1)`=e^{2x-1}+2xe^{2x-1}$

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NNNLLL54 6)y`=1/(3+sqrtx) * 1/(2sqrtx)

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