Answer:
To find the derivative of the function \(f(x) = (3x - 1)^2\) and then evaluate it at \(x = 2\), you can use the chain rule.
First, find the derivative of \(f(x)\) with respect to \(x\):
\(f(x) = (3x - 1)^2\)
Now, apply the chain rule:
\(f'(x) = 2(3x - 1)(3)\)
Simplify:
\(f'(x) = 6(3x - 1)\)
Now, evaluate \(f'(2)\):
\(f'(2) = 6(3(2) - 1)\)
\(f'(2) = 6(6 - 1)\)
\(f'(2) = 6(5)\)
\(f'(2) = 30\)
So, \(f'(2) = 30\).
Explanation: