Answer:
Therefore, the derivative of f(x) evaluated at x=5 is 0.202 to five decimal places.
Explanation:
The derivative of the function f(x)=5x^1/5x-1 can be found by using the power rule and chain rule. Applying the power rule, the derivative of the first part 5x^1 is 5x^0, which simplifies to 5.
Applying the chain rule, the derivative of the second part 1/5x-1 is (-1)*(1/5x-1)^2*1/5, which simplifies to 1/25x^2-2/5x. Combining the two parts, the derivative of f(x) is 5-1/25x^2+2/5x.
When evaluating f'(x) at the given value of x=5, the derivative simplifies to f'(5)=5-1/25(5)^2+2/5(5)=5-1/625+2/5=125/625+2/5=127/625=0.202.