Step 1:
To find the derivative of the function, apply the chain rule.
[tex]\frac{d\text{y}}{dx}\text{ = }\frac{dy}{du}\text{ }\times\text{ }\frac{du}{dx}[/tex][tex]\begin{gathered} \text{If y = x}^n \\ \frac{dy}{dx}=nx^{n-1} \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} y=(2x+1)^4 \\ \text{Let u = 2x + 1} \\ \text{Then y = u}^4 \\ \frac{du}{dx}\text{ = 2} \\ \frac{dy}{du}=4u^3 \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Therefore,} \\ \frac{dy}{dx}\text{ = 2 }\times4u^3 \\ =8u^3 \\ =8(2x+1)^3 \end{gathered}[/tex]Final answer
[tex]\text{The derivative of the function is = 8(2x + 1)}^3[/tex]