Given that $y$ is a function of $x$, differentiate the expression $\left(x^{2}+y^{2}\right)^{4}$ with respect to $x$. Enter $D$ for $\frac{dy}{dx}$ in your answer.

$\displaystyle \frac{d}{dx} \left[ \left(x^{2}+y^{2}\right)^{4} \right] =$