# How do you differentiate f(x) = (1-3sqrt(2x^2-1))^2  using the chain rule?

Nov 1, 2016

$f ' \left(x\right) = \frac{- 12 x \left(1 - 3 \sqrt{2 {x}^{2} - 1}\right)}{\sqrt{2 {x}^{2} - 1}}$
$f \left(x\right) = {\left(1 - 3 \sqrt{2 {x}^{2} - 1}\right)}^{2}$
$f ' \left(x\right) = 2 \left(1 - 3 \sqrt{2 {x}^{2} - 1}\right) \frac{- 3}{2 \sqrt{2 {x}^{2} - 1}} \cdot 4 x$
$f ' \left(x\right) = \frac{- 12 x \left(1 - 3 \sqrt{2 {x}^{2} - 1}\right)}{\sqrt{2 {x}^{2} - 1}}$