1 Answer

Daniel Gelling · Answer 1 · 2023-08-18T05:36:52+0000

the quotient rule say:

$((f(x))/(g(x)))^(\prime)=(g(x)\cdot f^(\prime)(x)-f(x)\cdot g^(\prime)(x))/((g(x))^2)$

now we defined:

$\begin{gathered} f(x)=-4x^2+16 \\ g(x)=(x^2+4)^2 \end{gathered}$

and the derivative:

$\begin{gathered} f^(\prime)(x)=-8x \\ g^(\prime)(x)=2\cdot(x^2+4)\cdot2x \\ g^(\prime)(x)=4x(x^2+4) \end{gathered}$

so now we can replace on the quotient rule:

$((x^2+4)^2\cdot(-8x)-4x(x^2+4)\cdot(-4x^2+16))/((x^2+4)^4)$

now we can use properties, like:

Please log in or register to add a comment.