# How do you differentiate y= (8/x^3)((x + x^7)/5)?

Jun 22, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{16}{5 {x}^{3}} + \frac{32}{5} {x}^{3}$

#### Explanation:

The function $y = \left(\frac{8}{x} ^ 3\right) \left(\frac{x + {x}^{7}}{5}\right)$

= $\frac{8}{5} \times \left(\frac{x + {x}^{7}}{x} ^ 3\right)$

= $\frac{8}{5} \times \left(\frac{x}{x} ^ 3 + {x}^{7} / {x}^{3}\right)$

= $\frac{8}{5} \times \left(\frac{1}{x} ^ 2 + {x}^{4}\right)$

Hence $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{8}{5} \times \left(\frac{- 2}{x} ^ 3 + 4 {x}^{3}\right)$

or $\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{16}{5 {x}^{3}} + \frac{32}{5} {x}^{3}$