the quotient rule say:
[tex](\frac{f(x)}{g(x)})^{\prime}=\frac{g(x)\cdot f^{\prime}(x)-f(x)\cdot g^{\prime}(x)}{(g(x))^2}[/tex]
now we defined:
[tex]\begin{gathered} f(x)=-4x^2+16 \\ g(x)=(x^2+4)^2 \end{gathered}[/tex]
and the derivative:
[tex]\begin{gathered} f^{\prime}(x)=-8x \\ g^{\prime}(x)=2\cdot(x^2+4)\cdot2x \\ g^{\prime}(x)=4x(x^2+4) \end{gathered}[/tex]
so now we can replace on the quotient rule:
[tex]\frac{(x^2+4)^2\cdot(-8x)-4x(x^2+4)\cdot(-4x^2+16)}{(x^2+4)^4}[/tex]
now we can use properties, like:
[tex](x^2+4)^2=x^4+8x+16[/tex]
