Find the derivative of 1/ x.

Solution:

The derivative of a function is represented by or f '(x). It means that the function is the derivative of y with respect to the variable x.

Let us consider f(x) = 1/x =x^-1

Then, f'(x) = n x^{n - 1} , where n = -1.

Replacing n with -1, we get

f'(1/x) = -1 x^-2   

f'(1/x) = -1/ x²

So, the derivative of 1/x is -1/x².

Find the derivative of 1/ x.

Summary:

The derivative of 1/x is -1/x².