# How do you find the derivative of r= 2theta sqrt(sec theta) using the chain rule?

Sep 16, 2017

$\frac{\mathrm{dr}}{d \theta} = \sqrt{\sec} \theta \left(2 + \theta \tan \theta\right)$
$r = 2 \theta \sqrt{\sec} \theta$
Differentiating both sides with respect to $\theta$ we get
(dr)/(d theta)=2sqrtsectheta + 2theta×1/(2sqrtsectheta)secthetatantheta
$= 2 \sqrt{\sec} \theta + \theta \sqrt{\sec} \theta \tan \theta$
$= \sqrt{\sec} \theta \left(2 + \theta \tan \theta\right)$