Chapter 7 - Section 7.3 - Hyperbolic Functions - Exercises - Page 417: 35

$|sec x|$

We are given: $y=sinh^{-1} (\tan x)$ Recall the formula: $\dfrac{d (\sinh^{-1} x)}{dx}=\dfrac{1}{ \sqrt{1 + x^2}}$ We need to use the chain rule to get the differentiation: Thus, $\dfrac{dy}{d x}=\dfrac{1}{ \sqrt{1 + (\tan x)^2}}(sec^2 x)=\dfrac{1}{ \sqrt{ sec^2 x}}(sec^2 x) =|sec x|$