# What is the second derivative of f(x)= 8/x-2?

Dec 10, 2015

$\frac{16}{{x}^{3}}$

#### Explanation:

The first derivative is:
$\frac{d}{\mathrm{dx}} \frac{8}{x} - \frac{d}{\mathrm{dx}} 2$

Rewriting,
$\frac{d}{\mathrm{dx}} 8 \cdot {x}^{-} 1 - \frac{d}{\mathrm{dx}} 2$

Using derivative rules, and the fact that the derivative of any constant is zero,
$8 \cdot \frac{d}{\mathrm{dx}} {x}^{-} 1 - 0$

Using the power rule to finish,
$- 8 \cdot {x}^{-} 2$

This is our first derivative. To find the second, we simply take the derivative of the above expression:
$\frac{d}{\mathrm{dx}} - 8 {x}^{-} 2$

All we need to do is use the power rule again:
$16 {x}^{-} 3$

In another form:
$\frac{16}{{x}^{3}}$

And we're done.