Question

O valor de f'(x) da função f(x) = 3(9x-4)^4, é: (REGRA DA CADEIA)

Answer 1

$Seja~~w(x)~=~9x-4\\\\\\Temos:\\\\\\\frac{df(x)}{dx}~=~\frac{df(w(x))}{dw}~.~\frac{dw(x)}{dx}\\\\\\\frac{df(x)}{dx}~=~\left(~3(w(x))^4~\right)'~.~(~w(x)~)'\\\\\\\frac{df(x)}{dx}~=~\left(~3(w(x))^4~\right)'~.~(~9x-4~)'\\\\\\\frac{df(x)}{dx}~=~4~.~3.(~w(x)~)^{4-1}~.~(9)\\\\\\\frac{df(x)}{dx}~=~12.(~9x-4~)^3~.~9\\\\\\\boxed{\frac{df(x)}{dx}~=~108.(9x-4)^3}$