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

Jan 24, 2016

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

#### Explanation:

differentiating using the 'chain rule ' :

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

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

Jan 24, 2016

$f ' \left(x\right) = - 3 {\sec}^{2} \left(1 - 3 x\right)$
Using the general rule $\frac{d}{\mathrm{dx}} \tan \left[u \left(x\right)\right] = {\sec}^{2} u \cdot \frac{\mathrm{du}}{\mathrm{dx}}$,
we get $\frac{d}{\mathrm{dx}} \tan \left(1 - 3 x\right) = - 3 {\sec}^{2} \left(1 - 3 x\right)$