# How do you differentiate  y =(−7 x^2 − 5)^8  using the chain rule?

Dec 13, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 112 x {\left(- 7 {x}^{2} - 5\right)}^{7}$

#### Explanation:

Applying the chain rule gives us

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} {\left(- 7 {x}^{2} - 5\right)}^{8}$

$= 8 {\left(- 7 {x}^{2} - 5\right)}^{7} \left(\frac{d}{\mathrm{dx}} \left(- 7 {x}^{2} - 5\right)\right)$

$= 8 {\left(- 7 {x}^{2} - 5\right)}^{7} \left(- 14 x\right)$

So

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 112 x {\left(- 7 {x}^{2} - 5\right)}^{7}$