Question

qual a derivada de 4/5x+2

Answer 1

$\mathtt{f(x)=\dfrac{4}{5x+2}}$


Vamos usar a Regra do Quociente para derivar:

$\mathtt{f'(x)=\left(\dfrac{4}{5x+2} \right )'}\\\\\\ \mathtt{f'(x)=\dfrac{(4)'\cdot (5x+2)-4\cdot (5x+2)'}{(5x+2)^2}}\\\\\\ \mathtt{f'(x)=\dfrac{0\cdot (5x+2)-4\cdot 5}{(5x+2)^2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathtt{f'(x)=-\,\dfrac{20}{(5x+2)^2}} \end{array}}$


Dúvidas? Comente.


Bons estudos! :-)