# What is the second derivative of f(x)= 1/x^3-x^3?

Jan 26, 2016

$\frac{12}{{x}^{5}} - 6 x$

#### Explanation:

I would change the function to

${x}^{-} 3 - {x}^{3}$

Now, we now that the derivate of

${x}^{a}$ is $a \cdot {x}^{a - 1}$

we can calculate the first derivate

$- 3 \cdot {x}^{-} 4 - 3 \cdot {x}^{2}$

and the second derivative as:

$- 3 \cdot \left(- 4\right) \left({x}^{-} 5\right) - \left(3 \cdot 2 \cdot x\right)$

$12 \left({x}^{-} 5\right) - 6 x$ or

$\frac{12}{{x}^{5}} - 6 x$