Question

How do you derive `y = 1/x` using the quotient rule?

Answer 1

See the explanation section below.

Explanation:

The quotient rule tells us that the derivative of `f/g` is

`(f'g-fg')/g^2`

Applying this to `1/x` we note

`f(x) = 1`, so `f'(x) = 0`, and

`g(x) = x`, so g'(x) = 1#

`d/dx(1/x) = ((0)(x) - (1) (1))/x^2 = -1/x^2`