Question

Найти производную y=√x(-2x+1)

Answer 1

$y'=sqrt{x}left(-2x+1right):\\frac{d}{dx}left(sqrt{x}left(-2x+1right)right) = \=frac{d}{dx}left(sqrt{x}right)left(-2x+1right)+frac{d}{dx}left(-2x+1right)sqrt{x} =\=frac{d}{dx}left(x^{frac{1}{2}}right)left(-2x+1right)+ (-frac{d}{dx}left(2xright)+frac{d}{dx}left(1right))sqrt{x} =\frac{1}{2}x^{frac{1}{2}-1}left(-2x+1right)+(-2+0)sqrt{x}=\| :: frac{1}{2}x^{frac{1}{2}-1} =frac{1}{2}x^{-frac{1}{2}}=frac{1}{2}cdot frac{1}{sqrt{x}}=frac{1}{2sqrt{x}}$

$=frac{1}{2sqrt{x}}left(-2x+1right)+left(-2right)sqrt{x} = \=frac{-2x+1}{2sqrt{x}}-2sqrt{x}=\=frac{-2x+1-2sqrt{x}cdot :2sqrt{x}}{2sqrt{x}}=\=frac{-6x+1}{2sqrt{x}}$