To find the derivative of the function f(x) = 1/x, we can use the power rule of differentiation. First, we rewrite the function in a form that makes it easier to differentiate:
f(x) = x-1
Now, we apply the power rule, which states that if you have a function in the form of xn, its derivative f'(x) is n*xn-1.
In our case, n = -1. Therefore, we differentiate:
f'(x) = -1 * x-1-1 = -1 * x-2
This simplifies to:
f'(x) = -1/x2
So, the derivative of 1/x is -1/x2.