Question

Derivada de
$y=x(1-2x)^6$

Answer 1

y = x(1 -2x)⁶

y ' = x'(1-2x)⁶ + x[(1-2x)⁶]'(-2x)'

y' = 1(1-2x)⁶ +x*6*(1-2x)⁶⁻¹*(-2)

y' = (1-2x)⁶ +6x(1-2x)⁵*-2

y' = (1-2x)⁶ -12x(1-2x)⁵*

$\\ y' = (1-2x)^5[ -12x + (1-2x)] \\ \\ y' = (1-2x)^5(-12x+1-2x) \\ \\ y' = (1-2x)^5(1-14x)$