# What is the second derivative of f(x)= 8/x-2x^3?

May 26, 2018

$f ' ' \left(x\right) = \frac{16}{x} ^ 3 - 12 x$

#### Explanation:

$\text{differentiate using the "color(blue)"power rule}$

•color(white)(x)d/dx(ax^n)=nax^(n-1)

$f \left(x\right) = \frac{8}{x} - 2 {x}^{3} = 8 {x}^{-} 1 - 2 {x}^{3}$

$f ' \left(x\right) = - 8 {x}^{-} 2 - 6 {x}^{2}$

$f ' ' \left(x\right) = 16 {x}^{-} 3 - 12 x = \frac{16}{x} ^ 3 - 12 x$