# How do you differentiate f(x)= ( -2x^2+ 3x ) / ( 4e^x + 2 )  using the quotient rule?

Set $u \left(x\right) = - 2 {x}^{2} + 3 x$ and $v \left(x\right) = 4 {e}^{x} + 2$ then the quotient rule
says that the first derivative of $f \left(x\right) = \frac{u \left(x\right)}{v \left(x\right)}$ is
$f ' \left(x\right) = \frac{u ' \left(x\right) \cdot v \left(x\right) - u \left(x\right) \cdot v ' \left(x\right)}{v {\left(x\right)}^{2}}$
where $u ' \left(x\right) = - 4 x + 3$ and $v ' \left(x\right) = 4 \cdot {e}^{x}$