Question

calculo de derivada. somente a 51

Answer 1

Usando a regra do quociente

$y =\frac{3x+4}{x+1}$

$u=3x+4~~~~~~~~u'=3\\v=x+1~~~~~~v'=1$

$f'(x)= \frac{u'*v-u*v'}{v^2}\\ \\ \\f'(x)= \frac{3*(x+1)-(3x+4)*1}{(x+1)^2}$

$f'(x)= \frac{3x+3-3x-4}{(x+1)^2}$

$\boxed{f'(x)=- \frac{1}{(x+1)^2} }$