Final answer:
To find the derivative of the given function, we can use the quotient rule. To find f'(5), substitute x=5 into the derivative expression.
Step-by-step explanation:
To find the derivative of f(x)= x² -3x +2/x²-2, we can use the quotient rule. The quotient rule states that if we have a function of the form f(x) = g(x)/h(x), then the derivative of f(x) is given by f'(x) = (g'(x)h(x) - g(x)h'(x))/[h(x)]². Applying this rule to our function, we have f'(x) = [(2x)(x²-2)-(x²-3x+2)(2x)]/(x²-2)².
To find f'(5), we substitute x=5 into the derivative expression we obtained earlier: f'(5) = [(2(5))(5²-2)-((5²-3(5)+2)(2(5)))]/(5²-2)².