calculate the derivative of the function.\n\n$f(x)=(8x - 1)^2$\n\n$f(x)=$

Explanation:

Step1: Use the chain - rule

Let $u = 8x - 1$, then $f(x)=u^{2}$. The chain - rule states that $\frac{df}{dx}=\frac{df}{du}\cdot\frac{du}{dx}$.

Step2: Find $\frac{df}{du}$

If $f(u)=u^{2}$, then $\frac{df}{du}=2u$.

Step3: Find $\frac{du}{dx}$

If $u = 8x - 1$, then $\frac{du}{dx}=8$.

Step4: Calculate $\frac{df}{dx}$

Substitute $u = 8x - 1$ back into $\frac{df}{du}$ and multiply by $\frac{du}{dx}$. So $\frac{df}{dx}=2u\times8=2(8x - 1)\times8$. Simplify the expression: $\frac{df}{dx}=16(8x - 1)=128x-16$.

Answer:

$128x - 16$