Question

find the first and the second derivatives of the function.
$f(x)=(8x + 1)^{3}$
$f(x)=3(8x + 1)^{2}(8)$
$f(x)=\square$

Explanation:

Step1: Differentiate \(f'(x)\)

Use the chain rule again. Let \(u = 8x + 1\), so \(f'(x)=24(8x + 1)^{2}\). The derivative of \(y = 24u^{2}\) with respect to \(x\) is \(y'=24\times2u\times8\).

Step2: Simplify the expression

Substitute \(u = 8x + 1\) back into the derivative. \(24\times2\times8\times(8x + 1)=384(8x + 1)\)

Answer:

\(384(8x + 1)\)