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

Oct 28, 2015

See the explanation section below.

Explanation:

The quotient rule tells us that the derivative of $\frac{f}{g}$ is

$\frac{f ' g - f g '}{g} ^ 2$

Applying this to $\frac{1}{x}$ we note

$f \left(x\right) = 1$, so $f ' \left(x\right) = 0$, and

$g \left(x\right) = x$, so g'(x) = 1#

$\frac{d}{\mathrm{dx}} \left(\frac{1}{x}\right) = \frac{\left(0\right) \left(x\right) - \left(1\right) \left(1\right)}{x} ^ 2 = - \frac{1}{x} ^ 2$