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

$f ' \left(x\right) = \frac{{e}^{\tan \left(\ln x\right)} {\sec}^{2} \left(\ln x\right)}{x}$
$f ' \left(x\right) = \left({e}^{\tan \left(\ln x\right)}\right) ' = {e}^{\tan \left(\ln x\right)} \cdot \left(\tan \left(\ln x\right)\right) ' = {e}^{\tan \left(\ln x\right)} \cdot {\sec}^{2} \left(\ln x\right) \cdot \left(\ln x\right) ' = {e}^{\tan \left(\ln x\right)} \cdot {\sec}^{2} \left(\ln x\right) \cdot \frac{1}{x}$
$f ' \left(x\right) = \frac{{e}^{\tan \left(\ln x\right)} {\sec}^{2} \left(\ln x\right)}{x}$