# How do you differentiate y = x^5 + (7 − x)^5?

Apr 13, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 \left({x}^{4} - {\left(7 - x\right)}^{4}\right)$

#### Explanation:

$y = {x}^{5} + {\left(7 - x\right)}^{5}$

Apply power rule and chain rule.

$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 {x}^{4} + 5 {\left(7 - x\right)}^{4} \cdot \frac{d}{\mathrm{dx}} \left(7 - x\right)$

$= 5 {x}^{4} + 5 {\left(7 - x\right)}^{4} \cdot \left(0 - 1\right)$

$= 5 \left({x}^{4} - {\left(7 - x\right)}^{4}\right)$