# How do you find the derivative of f(x)=(8x^2-6)^-1?

Jun 16, 2016

$\frac{\mathrm{df}}{\mathrm{dx}} = - \frac{16 x}{8 {x}^{2} - 6} ^ 2$

#### Explanation:

We use the chain rule here.

As $f \left(x\right) = {\left(8 {x}^{2} - 6\right)}^{- 1}$

$\frac{\mathrm{df}}{\mathrm{dx}} = - 1 \times {\left(8 {x}^{2} - 6\right)}^{- 1 - 1} \times \left(16 x\right)$ or

= $- \frac{1}{8 {x}^{2} - 6} ^ 2 \times \left(16 x\right)$

= $- \frac{16 x}{8 {x}^{2} - 6} ^ 2$