# Find the differential of y in the function: y=(x^3-2)^2 ?

## thx

Apr 9, 2018

To differentiate this function the function of a function rule can be used or the function can be expanded and differentiate.

#### Explanation:

The first way is as follows:

$y = {\left({x}^{3} - 2\right)}^{2}$
$y ' = 2 \left({x}^{3} - 2\right) \times 3 {x}^{2}$

Therefore:
$y ' = 6 {x}^{2} \left({x}^{3} - 2\right)$

The second method is as follows:

$y = {\left({x}^{3} - 2\right)}^{2}$
$y = {x}^{6} - 4 {x}^{3} - 4$
$y ' = 6 {x}^{5} - 12 {x}^{2}$

Therefore:
$y ' = 6 {x}^{2} \left({x}^{3} - 2\right)$