find the derivative of the function by first expanding the expression. f(x)=(8x - 5)^2 f(x)=□

Answer:

$128x - 80$

Explanation:

Step1: Expand the function

[ \begin{align*} f(x)&=(8x - 5)^2\ &=(8x - 5)(8x - 5)\ &=64x^2-40x-40x + 25\ &=64x^2-80x + 25 \end{align*} ]

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $y = 64x^2-80x + 25$, the derivative of $64x^2$ is $2\times64x^{2 - 1}=128x$, the derivative of $-80x$ is $-80\times1x^{1 - 1}=-80$, and the derivative of the constant 25 is 0. So $f^\prime(x)=128x-80$.