How do you differentiate f(x)=sqrtsec(e^(x) )  using the chain rule?

Jun 28, 2016

$= \frac{1}{2} {e}^{x} \sqrt{\sec {e}^{x}} \cdot \tan {e}^{x}$

Explanation:

${\left(\sqrt{\sec} \left({e}^{x}\right)\right)}^{p} r i m e$

using the chain rule and doing it bit by bit....

$= \frac{1}{2} \frac{1}{\sqrt{\sec {e}^{x}}} \cdot {\left(\sec {e}^{x}\right)}^{p} r i m e$

$= \frac{1}{2} \frac{1}{\sqrt{\sec {e}^{x}}} \cdot \sec {e}^{x} \tan {e}^{x} \cdot {\left({e}^{x}\right)}^{p} r i m e$

$= \frac{1}{2} \frac{1}{\sqrt{\sec {e}^{x}}} \cdot \sec {e}^{x} \tan {e}^{x} \cdot {e}^{x}$

$= \frac{1}{2} {e}^{x} \sqrt{\sec {e}^{x}} \cdot \tan {e}^{x}$