Question

Por favor alguém me ajude nessa questão

e40608fdf98a66defd1aa70a713ce862.docx

Answer 1

Expressão:

$f_{(x)}=\dfrac{6x^2}{4x-x^2}\\\\\\ Aplicando\ derivada\ em fra\c{c}\~ao:\\\\ f'_{(x)}=\dfrac{v.u'-u.v'}{v^2}\\\\ Onde:\\ u=6x^2\\ v=4x-x^2$

Derivando:

$f'_{(x)}=\dfrac{(4x-x^2).(6x^2)'-(6x^2).(4x-x^2)'}{(4x-x^2)^2}\\\\\\ f'_{(x)}=\dfrac{(4x-x^2).(12x)-(6x^2).(4-2x)}{(4x-x^2)^2}\\\\\\ f'_{(x)}=\dfrac{48x^2-12x^3-24x^2+12x^3}{16x^2-8x^3+x^4}\\\\\\ f'_{(x)}=\dfrac{24x^2}{x^2(x^2-8x+16)}\\\\\\ f'_{(x)}=\dfrac{24}{(x^2-8x+16)}\\\\\\ \boxed{f'_{(x)}=\dfrac{24}{(x-4)^2}}$

Espero ter ajudado.
Bons estudos!