Find the indicated derivative of the following function:𝑓(𝑥)=1𝑥𝑓(4)(𝑥)=

The function given is f(x) = 1/x.

To find the fourth derivative of the function, we first need to find the first, second, and third derivatives.

1. First derivative: The derivative of f(x) = 1/x is found using the power rule for derivatives, which states that the derivative of x^n is nx^(n-1). In this case, 1/x is the same as x^-1, so its derivative is -1x^-2, or -1/x^2.

So, f'(x) = -1/x^2.

2. Second derivative: Applying the power rule again, the derivative of -1/x^2 is 2/x^3.

So, f''(x) = 2/x^3.

3. Third derivative: Applying the power rule once more, the derivative of 2/x^3 is -6/x^4.

So, f'''(x) = -6/x^4.

4. Fourth derivative: Finally, applying the power rule one last time, the derivative of -6/x^4 is 24/x^5.

So, f''''(x) = 24/x^5.

Therefore, the fourth derivative of the function f(x) = 1/x is f''''(x) = 24/x^5.