Final answer:
The derivative of the function g(x) = 13 - 5 ln(x) is found by applying rules of differentiation to each term separately, resulting in g'(x) = -5/x.
Step-by-step explanation:
To find the derivative of the function g(x) = 13 - 5 ln(x), you would use the rules of differentiation for each term independently. For the constant 13, the derivative is 0 since the slope of a constant is always zero. For the term involving the natural logarithm, recall that the derivative of ln(x) with respect to x is 1/x.
Thus, using the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function, the derivative of -5 ln(x) is -5/x. So, putting it all together, the derivative g'(x) is:
g'(x) = 0 - 5/x = -5/x