Final answer:
To find f'(x), apply the chain rule. The derivative of ln(u) is 1/u * du/dx. Substitute x = 8 to find the exact value of f'(8) as -2.25.
Step-by-step explanation:
To find f'(x), we need to apply the chain rule. The derivative of ln(u) is 1/u * du/dx. Here, u is 71x. So, the derivative of -18ln(71x) can be found by multiplying -18 with the derivative of ln(71x). Using the chain rule, we get:
f'(x) = -18 * (1/(71x)) * 71
f'(x) = -18/ x
To find the value of f'(8), we substitute x = 8 in the derivative formula:
f'(8) = -18/ 8
f'(8) = -2.25