Question

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)

Answer 1

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