Question

Calcule a derivação da função abaixo pela definição:

$f(x) = \dfrac{x-3}{2x+4}$

Answer 1

$\sf \displaystyle f\left(x\right)=\frac{x-3}{2x+4}\\\\\\\\\sf \frac{d}{dx}\left(\frac{x-3}{2x+4}\right)\\\\\\\\\sf \boxed{\sf Aplique\:a\:regra\:do\:quociente\Rightarrow\quad \left(\frac{f}{g}\right)^'=\dfrac{f\:'\cdot g-g'\cdot f}{g^2}}\\\\\\\\\sf \frac{\dfrac{d}{dx}\left(x-3\right)\left(2x+4\right)-\dfrac{d}{dx}\left(2x+4\right)\left(x-3\right)}{\left(2x+4\right)^2}\\\\\\\\\sf \frac{d}{dx} (x-3)=1\\\\\\\\\sf \sf \frac{d}{dx}(2x+4)=2$

$\sf \dfrac{1\cdot \left(2x+4\right)-2\left(x-3\right)}{\left(2x+4\right)^2}\\\\\\\\\sf Simplificar\\\\\\\\\boxed{\boxed{\sf S_1=\{ \frac{5}{2\left(x+2\right)^2}\}}}$

• Caso tenha bugado acesse o link >> https://brainly.com.br/tarefa/42363913
• OU VEJA O ANEXO