Find the derivative of the function $y=\sin (8x^4+7x-3)$.

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

$y=\tan \left(8x^4\right)$

Determine the equation of the line tangent to the graph of $y=x\sqrt{17-x^2}$ at the point $(1,4)$.

Calculate the derivative of the function $g\left(t\right)=e^{2t+\tan t-4}$.

Determine the derivative of $p=\cos \left(\frac{2x}{\sqrt{2x+1}}\right)$.

Given that $f(-1)=-1$, $f^{\prime }(-1)=-2$, $g(-1)=-1$, and $g^{\prime }(-1)=5$, find the derivative of $f^4\left(x\right)g\left(x\right)$ at $x=-1$.

What is the derivative of the following function?

$q=\sqrt{4-x^2}$