Question

Derivada de
$y= \frac{1}{4} x^5(1-2x)$ 

Answer 1

$\\ y = \frac{1}{4} *x^5(1-2x) \\ \\ y' = \frac{1}{4} *x^5'(1-2x) + \frac{1}{4} *x^5*(1-2x)' \\ \\ y' = \frac{1}{4} *5*x^5^-^1(1-2x)+ \frac{x^5}{4}*(0-2) \\ \\ y' = \frac{5x^4(1-2x)}{4} + \frac{x^5}{4}*(-2) \\ \\ y' = \frac{5x^4(1-2x)-2x^5}{4} \\ \\ y' = \frac{x^4[5(1-2x)-2x]}{4}$

Answer 2

$\sf \displaystyle y=\frac{1}{4}x^5\left(1-2x\right)\\\\\\\frac{d}{dx}\left(\frac{1}{4}x^5\left(1-2x\right)\right)\\\\\\=\frac{1}{4}\frac{d}{dx}\left(x^5\left(1-2x\right)\right)\\\\\\=\frac{1}{4}\left(\frac{d}{dx}\left(x^5\right)\left(1-2x\right)+\frac{d}{dx}\left(1-2x\right)x^5\right)\\\\\\=\frac{1}{4}\left(5x^4\left(1-2x\right)+\left(-2\right)x^5\right)\\\\\\\to \boxed{\sf =\frac{5x^4-12x^5}{4}}$