Question

resolver las siguientes derivadas algebraicas(abrir imagen):)​

Answer 1

1)

$y=(\frac{2-4x}{5-2x})^3\\y'=3(\frac{2-4x}{5-2x})^2[\frac{(-4)(5-2x)-(-2)(2-4x)}{(5-2x)^2}]\\y'=3\frac{(2-4x)^2}{(5-2x)^2}[\frac{-20+8x+4-8x}{(5-2x)^2}]\\y'=3\frac{(2-4x)^2}{(5-2x)^2}(\frac{-16}{(5-2x)^2})\\y'=-48\frac{(2-4x)^2}{(5-2x)^4}\\y'=-192\frac{(1-2x)^2}{(5-2x)^4}$

2)

$f(x)=(2x^3+2)^3(6x)\\f'(x)=3(2x^3+2)^2(6x^2)(6x)+6(2x^3+2)^3\\f'(x)=108(2x^3+2)^2(x^3)+6(2x^3+2)^3\\f'(x)=(108x^3+12x^3+12)(2x^3+2)^2\\f'(x)=(120x^3+12)(2x^3+2)^2\\f'(x)=48(10x^3+1)(x^3+1)^2$