Identify the inner function $u = g(x)$, and the outer function $y = f(u)$ for the composition $y = f(g(x))$. Then, find $\frac{\mathrm{dy}}{\mathrm{dx}}$:
$y=\tan \left(8x^4\right)$

$u=8x^4$; $f\left(u\right)=\sec u$; $\frac{dy}{dx}=32x^3{\sec }^2\left(8x^4\right)$

$u=8x$; $f\left(u\right)=\sec u$; $\frac{dy}{dx}=32x^3{\sec }^2\left(8x^4\right)$

$u=8x^4$; $f\left(u\right)=\tan u$; $\frac{dy}{dx}=32x^4{\sec }^2\left(8x^4\right)$

$u=8x^4$; $f\left(u\right)=\tan u$; $\frac{dy}{dx}=32x^3{\sec }^2\left(8x^4\right)$