Question

Find the derivative of :(2x+1)⁴

Answer 1

Step 1:

To find the derivative of the function, apply the chain rule.

`\frac{d\text{y}}{dx}\text{ = }(dy)/(du)\text{ }*\text{ }(du)/(dx)`
`\begin{gathered} \text{If y = x}^n \\ (dy)/(dx)=nx^(n-1) \end{gathered}`

Step 2:

`\begin{gathered} y=(2x+1)^4 \\ \text{Let u = 2x + 1} \\ \text{Then y = u}^4 \\ (du)/(dx)\text{ = 2} \\ (dy)/(du)=4u^3 \end{gathered}`

Step 3:

`\begin{gathered} \text{Therefore,} \\ (dy)/(dx)\text{ = 2 }*4u^3 \\ =8u^3 \\ =8(2x+1)^3 \end{gathered}`

Final answer

`\text{The derivative of the function is = 8(2x + 1)}^3`