# How do you differentiate y = (x^3 + 4)(-x^6 + x^4)?

Oct 14, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 9 {x}^{8} - 24 {x}^{5} + 7 {x}^{6} + 16 {x}^{3}$

#### Explanation:

The easiest way is to simply multiply the two brackets

$y = - {x}^{9} - 4 {x}^{6} + {x}^{7} + 4 {x}^{4}$

And then take the derivative of polinomials like this

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 9 {x}^{8} - 24 {x}^{5} + 7 {x}^{6} + 16 {x}^{3}$

You could use the product rule but this is a case where the simplest way is to foil the multiplication and then derive the result.