# How do you differentiate f(x)=-3tan4x^2 using the chain rule?

Oct 28, 2015

$f ' \left(x\right) = - 24 x {\sec}^{2} \left(4 {x}^{2}\right)$

#### Explanation:

Pull the constant out front

$f \left(x\right) = - 3 \cdot \tan \left(4 {x}^{2}\right)$

Take the derivative of the outside, $\tan$

$- 3 f ' \left(x\right) = - 3 \cdot {\sec}^{2} \left(4 {x}^{2}\right)$

Multiply the outside by the derivative of the inside, $4 {x}^{2}$

$f ' \left(x\right) = - 3 \cdot {\sec}^{2} \left(4 {x}^{2}\right) \left(8 x\right)$

$f ' \left(x\right) = \left(- 3\right) {\sec}^{2} \left(4 {x}^{2}\right) \left(8 x\right)$

Simplify

$f ' \left(x\right) = - 24 x {\sec}^{2} \left(4 {x}^{2}\right)$