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

Jan 10, 2016

$\left(- 6 x\right) {\sec}^{2} \left(1 - 3 {x}^{2}\right)$

#### Explanation:

applying the chain rule as follows :

$f ' \left(x\right) = {\sec}^{2} \left(1 - 3 {x}^{2}\right) . \frac{d}{\mathrm{dx}} \left(1 - 3 {x}^{2}\right)$

$f ' \left(x\right) = {\sec}^{2} \left(1 - 3 {x}^{2}\right) . \left(- 6 x\right)$

$\Rightarrow f ' \left(x\right) = \left(- 6 x\right) {\sec}^{2} \left(1 - 3 {x}^{2}\right)$